# Abstract computational model

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

A finite-state computational model describes possible executions through its state set, initial-state set, step relation and halt-state set.

mko-computational-model · definition · v0.10.0



## Mathematical statement

The finite abstract model in this entry is (S,Init,Step,Halt), with Init,Halt⊆S and Step⊆S×S. Executions start in Init and follow Step; a stuck state without successors is not automatically a member of Halt.





## Representative formula (exact TeX)

R\subseteq S





## Assumptions


- S is an explicitly given finite set, and Step is a directed relation that may be nondeterministic.
- Reaching Halt stops execution: truncate all outgoing edges from halts before analysis, even if the raw data contains them.





## Symbol scope


- R — step relation
- S — state set





## Intuition, definition, and misconceptions

Reachability begins at every initial state and follows zero or more permitted steps, with the declared halt truncation.

A legal trace starts in Init and has adjacent states related by Step. Once it enters Halt, that execution ends and cannot continue.

Failure to see a cycle at finite exploration depth does not prove that all executions terminate. A reachable nonhalting cycle or reachable stuck nonhalt is a termination risk.

A state with no outgoing edge is not automatically a halt, and a finite execution prefix does not establish all-path termination.





## Adopted derivation guide

[Abstract computational model: truncating halt edges, computing reachability and separating halting, stuck and non-terminating runs in a seven-state model](https://ocme.evemisslab.com/en/derivations/derivation-mko-computational-model-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Set](https://ocme.evemisslab.com/en/mko/mko-set/) — State, initial and halt conditions are represented by sets.
- [Binary relations and set projections](https://ocme.evemisslab.com/en/mko/mko-relation/) — Step semantics is a directed relation between states.
- [Natural number](https://ocme.evemisslab.com/en/mko/mko-natural-number/) — Natural numbers index finite trace lengths and step counts.





## Verification boundary

The entire reachable structure of a finite state graph can be enumerated; this implies no unspecified Turing completeness or behavior of a real program.

not_formalized

This does not mean the content is false; it means no replayable computational or formal evidence is registered yet.





## Next obligation

Develop layered deterministic/nondeterministic, stuck-state, maximal-execution and effective-encoding models.





## Same-source structured data

This page and the interactive view use the same object and existing language edition; this adds no proof or human review.

[Canonical MKO JSON](https://ocme.evemisslab.com/data/mko/computational-model.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-computational-model/index.md)