DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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 set cover decision problem

Definition

An instance of SET COVER consists of a finite set $U = {u_{1}, \dots, u_{m}},$ a family of subsets $S = {S_{1}, \dots, S_{n}} \subseteq P (U),$ and a natural number $k$ . It is a yes-instance when there exist indices $i_{1}, \dots, i_{t}$ with $t \leq k$ such that $S_{i_{1}} \cup \dots \cup S_{i_{t}} = U .$

Used by

Vertex cover polynomial-time many-one reduces to set cover Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Fabrizio Iozzi and Luca Trevisan, Handout NP3 (standard reference, not scraped)