Alphabeta MathHow 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.
The CFG equivalence and ambiguity problems
Definition
The CFG equivalence problem asks, given two context-free grammars and over the same alphabet, whether
The CFG ambiguity problem asks, given a context-free grammar , whether is ambiguous in the sense of Ambiguous grammars, unambiguous grammars, and inherently ambiguous languages.
Remarks
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Equivalence is a problem about pairs of grammars; ambiguity is a problem about one grammar.
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Normal-form conversions preserve the languages of grammars, but they do not by themselves answer either decision problem.
Depends on
Used by
- FALSE: CFG equivalence is decidable by normalization False statement
- CFG ambiguity is undecidable Theorem
- CFG equivalence is undecidable Theorem
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
- Alfred V. Aho, COMS W3261 CS Theory, Lecture 11 (standard reference, not scraped)
- H. Conrad Cunningham, CSci 311, Models of Computation, Chapter 8 (standard reference, not scraped)