DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-02

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.

The class coNP

Definition

The class coNP is $c o N P : = {L \subseteq {0, 1}^{*} : {0, 1}^{*} ∖ L \in N P} .$

Remarks

The complement is taken inside the same ambient language space ${0, 1}^{*}$ .
Saying that $L \in c o N P$ is therefore equivalent to saying that nonmembership in $L$ has polynomially checkable certificates.

Depends on

The class NP via polynomial-time verifiers

Used by

P ⊆ NP ∩ coNP Proposition
Polynomial-time many-one reductions transfer P-, NP-, and coNP-membership Theorem

Dependency tree · two levels

3 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 17: Space Complexity, PSPACE, Savitch's Theorem (standard reference, not scraped)