DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-30

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.

Regular languages

Definition

Let $Σ$ be an alphabet. A language $L \subseteq Σ^{*}$ is regular when there exists a DFA $D$ over $Σ$ such that $L = L (D),$ where $L (D)$ is the recognized language of Acceptance of a word by a DFA and the recognized language.

Thus regularity is a property of a language over a fixed alphabet: the machine is a witness, not part of the language itself.

Depends on

Acceptance of a word by a DFA and the recognized language

Used by

Regular languages are closed under the Boolean operations over a fixed alphabet Corollary
Every finite language is regular Proposition

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

Jean Gallier and Jocelyn Quaintance, Introduction to the Theory of Computation: Some Notes for CIS511 (standard reference, not scraped)
John Watrous, Introduction to the Theory of Computing, Lecture 2 (standard reference, not scraped)