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.

Leftmost and rightmost derivations

Definition

Let $G = (V, Σ, P, S)$ be a context-free grammar, and suppose $x A y \Rightarrow_{G} x α y$ is one derivation step.

This step is leftmost when $x$ contains no variables, so the rewritten occurrence of $A$ is the leftmost variable in the sentential form. It is rightmost when $y$ contains no variables, so the rewritten occurrence of $A$ is the rightmost variable.

A finite derivation is a leftmost derivation when each of its steps is leftmost, and a rightmost derivation when each of its steps is rightmost.

Depends on

One-step derivation and finite derivation in a context-free grammar

Used by

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)
John Watrous, Introduction to the Theory of Computing, Lecture 8 (standard reference, not scraped)