Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07
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.
Sharp-P and Gap-P functions
Definition
A #P function maps each input to the number of accepting paths of a binary-branching polynomial-time nondeterministic machine. A GapP function is accepting paths minus rejecting paths of such a machine. Function values are represented in binary.
Used by
- Polynomial time with a Sharp-P oracle Definition
- Sharp-P is a language class False statement
- FP is contained in Sharp-P Proposition
- NP is contained in P with a Sharp-P oracle Proposition
- NumberSAT belongs to Sharp-P Proposition
- Sharp-P is closed under sum and product Proposition
- NumberSAT is Sharp-P-complete under parsimonious reductions Theorem
- PP is closed under complement Theorem
- PP is strict sign testing for Gap-P Theorem
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Arora and Barak, Computational Complexity: A Modern Approach (standard reference, not scraped)
- Lance Fortnow, Counting Complexity (standard reference, not scraped)