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 class NP via polynomial-time verifiers
Definition
The class NP is the set of languages that admit a polynomial-time verifier with polynomially bounded certificates in the sense of Polynomial-time verifiers with polynomially bounded certificates.
Remarks
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This is the verifier definition of NP. The equivalent nondeterministic machine definition is proved next.
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Every statement on this page about complements of NP-languages is taken inside the same ambient space .
Depends on
Used by
- NP-hard and NP-complete languages Definition
- The class coNP Definition
- The search problem attached to an NP verifier Definition
- FALSE: NP means not polynomial-time solvable False statement
- NP ⊆ PSPACE ⊆ EXP Proposition
- P ⊆ NP ∩ coNP Proposition
- Polynomial-time many-one reductions transfer P-, NP-, and coNP-membership Theorem
- The verifier and nondeterministic definitions of NP agree 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
- Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach (standard reference, not scraped)
- Michael Sipser, MIT 18.404J Theory of Computation, Lecture 14: P and NP, SAT, Poly-time Reducibility (standard reference, not scraped)