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.

Greibach normal form

Definition

A context-free grammar $G = (V, Σ, P, S)$ is in Greibach normal form when every production is of the form $A \to a α,$ where $A \in V$ , $a \in Σ$ , and $α$ is a possibly empty word of variables, together with the optional exception $S \to ε$ when $S$ does not occur on any right-hand side.

Remarks

In GNF, every nonempty derivation step emits one terminal immediately.
The optional start-symbol $ε$ -rule plays the same role here as in Chomsky normal form.

Depends on

Context-free grammars

Used by

Every context-free language has an equivalent grammar in Greibach normal form Theorem

Dependency tree · two levels

3 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)
CSC444 CFLs and PDAs (standard reference, not scraped)