Finite Transition Models, Halt Truncation, and Stuck States
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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261013-advance-20261019-r04-computational-model-foundations · 2026-10-13 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
1. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
2. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5]], [0, 1, 2, 3, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5]], [0, 1, 2, 3, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
3. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
4. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
5. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
6. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
7. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
8. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
9. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
10. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
11. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
12. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
13. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
14. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
15. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
16. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
17. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
18. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
19. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
20. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
21. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
22. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
23. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
24. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
25. Complete Reachability with Halt Outgoing Edges Truncated
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (n, normalized Init, normalized Halt, normalized raw Step, all reachable states). Include zero-step reachability.
View answer and explanation
(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])
Start from every initial state but never continue through a halt, even if raw outgoing edges are listed. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is (6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-reachable-states · candidate
26. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
27. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
28. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
29. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 6], [Yes, No], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
30. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
31. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
32. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
33. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 6], [Yes, No], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
34. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
35. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
36. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
37. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 6], [Yes, No], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
38. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
39. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
40. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
41. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 6], [Yes, No], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
42. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
43. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
44. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
45. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 6], [Yes, No], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
46. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
47. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 4]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 4], [Yes, Yes], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 4], [Yes, Yes], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
48. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5, 5], [Yes, Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes, No], Yes, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
49. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 6]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 6], [Yes, No], Yes, Yes, [No], No, No)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 6], [Yes, No], Yes, Yes, [No], No, No).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
50. Legal Finite Trace Prefix and Post-Halt Continuation Guard
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. trace=[0, 1, 2, 5]. Give (trace, per-state type mask, nonempty?, first state in Init?, per-adjacent-pair raw Step flags, continued after a halt?, legal prefix?). A legal prefix need not end at Halt.
View answer and explanation
([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes)
Separate raw edge existence from the rule prohibiting continuation after halt; an empty trace is not a valid execution prefix. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [Yes, Yes, Yes, Yes], Yes, Yes, [Yes, Yes, Yes], No, Yes).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-trace-qualification · candidate
51. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
52. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
53. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
54. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
55. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
56. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
57. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
58. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
59. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
60. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
61. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
62. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
63. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
64. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
65. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
66. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
67. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
68. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
69. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
70. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
71. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
72. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [5], [3], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
73. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
74. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
75. Reachable Halt, Stuck, and Active States
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable declared halts, reachable nonhalting states with no successor, reachable nonhalting states with successors).
View answer and explanation
([0, 1, 2, 5], [5], [], [0, 1, 2])
A nonhalting dead end remains stuck, not a successful halt. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [5], [], [0, 1, 2]).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-halt-stuck-classification · candidate
76. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
77. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
78. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
79. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 4, 5], [4], No, No, reachable stuck-nonhalting-state)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], No, No, reachable stuck-nonhalting-state).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
80. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
81. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], No, No, reachable stuck-nonhalting-state).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
82. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], No, Yes, all-finite-model-paths-reach-halt).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
83. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 4, 5], [], No, Yes, all-finite-model-paths-reach-halt)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], No, Yes, all-finite-model-paths-reach-halt).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
84. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
85. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
86. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
87. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
88. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
89. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
90. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
91. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [2, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
92. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
93. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
94. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
95. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [4], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
96. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
97. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 5], [3], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
98. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
99. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [0, 3], [3, 4], [4, 5], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 3, 4, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
100. All-Path Finite Termination and Reachable Nonhalting Cycles
Use the complete finite, possibly nondeterministic transition model S=Fin(6)={0,…,5}, Init=[0], Halt=[5], Step=[[0, 1], [1, 2], [2, 5], [2, 1], [1, 1]]. Normalize sets and ordered transition pairs. Execution stops at a declared Halt state, ignoring all of its outgoing edges. A stuck nonhalting state is not a successful halt; finite prefixes prove no general termination. Give (reachable states, reachable stuck states, reachable nonhalting cycle?, all paths reach Halt?, classification). A reachable cycle takes classification precedence over a stuck state, but retain both diagnostics.
View answer and explanation
([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle)
Inspect the entire reachable nonhalting graph; unreachable cycles and outgoing edges from halts do not create this obligation. Empty initial sets are treated vacuously. Finite/synthetic checks are not new general formal Evidence. The exact result, retaining the requested order, is ([0, 1, 2, 5], [], Yes, No, reachable-nonhalting-cycle).
Reviewed step-by-step derivation
Abstract computational model · qf-ext19-model-cycle-termination-risk · candidate
Canonical question JSONL · English JSONL · Validation report