# Turing-machine decision model

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

Under fixed deterministic single-tape semantics, a decider must halt on every legal input and return the correct accept/reject answer.

mko-turing-machine-decision-model · definition · v0.10.0



## Mathematical statement

Specify finite states, input/tape alphabets, blank, start, accept, reject and deterministic transitions [state,read,next,write,move]. Unlisted tape cells are blank, and configurations are [state,head,sparse nonblank tape]. Exact steps and finite traces concern their supplied input only. A global decider certificate needs an all-input strictly decreasing ranking or explicit step bound and answer correctness. A recognizer may loop on nonmembers. Bounded simulation failure proves neither rejection nor nontermination, and one halting trace does not certify a global decider.





## Representative formula (exact TeX)

T(M,w)=h





## Assumptions


- Moves are L/R/S, and accept/reject states have no outgoing transitions.
- The global positive family uses the exact scan-decider schema with ranking unscanned input cells plus1.





## Symbol scope


- T — Turing execution record
- M — deterministic single-tape machine
- w — input word
- h — halting outcome





## Intuition, definition, and misconceptions

Signature qualification and execution semantics are separate.

A finite trace is input-local evidence.

A decider needs global termination and answer-correctness certificates.

One halting trace or a finite budget without halting does not show that the whole machine is a decider or that the input is rejected.





## Adopted derivation guide

[A scan decider for an even number of ones](https://ocme.evemisslab.com/en/derivations/derivation-mko-turing-machine-decision-model-01/)The original MKO is retained. The guide has its own append-only revision and verification boundaries, not a new Lean proof.





## Prerequisites


- [Abstract computational model](https://ocme.evemisslab.com/en/mko/mko-computational-model/) — Use finite control and explicit step semantics.
- [Decision problem](https://ocme.evemisslab.com/en/mko/mko-decision-problem/) — Answers have a yes/no meaning.
- [Deterministic finite automaton](https://ocme.evemisslab.com/en/mko/mko-finite-automaton/) — Finite-state control supplies background.
- [Algorithm correctness](https://ocme.evemisslab.com/en/mko/mko-algorithm-correctness/) — Deciders need total correctness.





## Verification boundary

This slice claims no formal Church-Turing-thesis proof, general complexity bound or multitape equivalence.

not_formalized

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





## Next obligation

Add many-one reductions, undecidability and complexity.





## 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/turing-machine-decision-model.json) · [Plain Markdown](https://ocme.evemisslab.com/en/mko/mko-turing-machine-decision-model/index.md)