DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-29

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.

Finite alphabets, encoded inputs, and algorithms

Definition

Fix a finite alphabet $Σ$ . An encoded input is a finite word in $Σ^{*}$ . An algorithm on inputs from $Σ^{*}$ is a deterministic procedure that, for each input word, either halts with an output or runs forever. A decision algorithm for a set $L \subseteq Σ^{*}$ is one that halts on every input and outputs YES exactly on the words of $L$ .

Used by

Recursive and recursively enumerable languages Definition

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Charles F. Miller III, Decision Problems for Groups - Survey and Reflections (standard reference, not scraped)
Alex Bishop, Minicourse: On Decision Problems in Groups (standard reference, not scraped)