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.
Polynomial time with a Sharp-P oracle
Definition
is deterministic polynomial time with oracle access to the fixed -complete function of NumberSAT is Sharp-P-complete under parsimonious reductions. The machine may make polynomially many adaptive queries of polynomial length, each answered by the binary expansion of the integer value rather than by a membership bit. Equivalently, one may use any fixed function complete under polynomial-time parsimonious reductions; completeness makes the resulting class independent of that choice.
Depends on
Used by
- NP is contained in P with a Sharp-P oracle Proposition
Dependency tree · two levels
8 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
- Arora and Barak, Computational Complexity: A Modern Approach (standard reference, not scraped)
- Lance Fortnow, Counting Complexity (standard reference, not scraped)