Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Model-equivalence theorems support but do not prove the Church-Turing thesis
Remark
The Church-Turing thesis from The Church-Turing thesis is supported by the fact that many apparently different formal models turn out to have the same computational power. The equivalence of one-way and two-way tapes (One-way and two-way infinite tape conventions are equivalent), of nondeterministic and deterministic recognizability (Deterministic and nondeterministic Turing machines recognize the same languages), and of RAM/register programs with Turing machines (RAM/register computation and Turing computation agree), together with the existence of a universal interpreter (A universal Turing machine exists for the chosen coding), shows that the Turing model is robust under wide formal redesign.
What these theorems prove is agreement among formal notions. What they do not prove is that the informal phrase "effectively calculable" from The Church-Turing thesis has been exhausted by those formal notions. That extra bridge is the content of the thesis itself, not a consequence of the equivalence theorems alone.
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13 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem (standard reference, not scraped)
- Jean Gallier and Jocelyn Quaintance, Notes on Formal Languages, Automata, Computability, and Complexity (standard reference, not scraped)
- Charles Brubaker and Lance Fortnow, Church-Turing Thesis lesson notes (standard reference, not scraped)