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.

Acceptance by empty stack for a PDA

Definition

Let $M = (Q, Σ, Γ, δ, q_{0}, Z_{0}, F)$ be a PDA.

A word $w \in Σ^{*}$ is accepted by empty stack when there exists a state $q \in Q$ such that $(q_{0}, w, Z_{0}) ⊢_{M}^{*} (q, ε, ε) .$

The set of words accepted in this sense is denoted $N (M)$ .

Depends on

PDA configurations and one-step moves

Used by

FALSE: acceptance by final state and by empty stack are literally identical False statement
Acceptance by final state and by empty stack are equivalent for PDAs Theorem
Every context-free grammar has an equivalent PDA Theorem
Every PDA has an equivalent context-free grammar Theorem

Dependency tree · two levels

2 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)
Dexter C. Kozen, Automata and Computability (standard reference, not scraped)