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.

Nerode equivalence of words

Definition

Let $L \subseteq Σ^{*}$ be a language over an alphabet $Σ$ .

Two words $u, v \in Σ^{*}$ are Nerode-equivalent for $L$ when every right continuation tests membership in the same way: $u \equiv_{L} v ⟺ \forall x \in Σ^{*}, u x \in L ⟺ v x \in L .$

The equivalence classes of $\equiv_{L}$ are the Nerode classes of $L$ . Their number, finite or infinite, is the index of $\equiv_{L}$ .

Depends on

Used by

Dependency tree · two levels

6 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)
Eric Blais, Models of Computation, 20. Nonregular Languages (standard reference, not scraped)