DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-12

How 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.

Computably enumerable hardness and completeness under computable many-one reductions

Definition

Let $C$ be a language over a finite alphabet.

$C$ is c.e.-hard when every recognizable language $L$ satisfies $L \leq_{m} C .$
$C$ is c.e.-complete when $C$ is recognizable and c.e.-hard.

Here "c.e." means "computably enumerable," which on this page is synonymous with "recognizable."

Depends on

Used by

The Turing-machine acceptance problem is computably enumerable complete Theorem

Dependency tree · two levels

4 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

Kevin Kelly, Many-one Reduction (standard reference, not scraped)
MIT 6.045J / 18.400J, Lecture 9: Mapping Reducibility and Rice's Theorem (standard reference, not scraped)