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.
FALSE: the Cook-Levin reduction enumerates all nondeterministic branches
Statement
The Cook-Levin reduction works by explicitly enumerating every nondeterministic branch of the machine.
Facts & Assumptions
Given: The Cook-Levin tableau encoding.
A bounded computation tableau records one computation branch of the machine, not the whole branch tree, by A bounded computation tableau for a nondeterministic Turing-machine run.
The Cook-Levin formula is satisfiable exactly when at least one accepting tableau exists, by The Cook-Levin formula is satisfiable if and only if an accepting bounded tableau exists.
Refutation
By [L1], one satisfying assignment describes one tableau, hence one branch. There is no requirement that the encoding simultaneously list all other branches.
By [L2], the reduction asks only whether some accepting tableau exists. Existence of one accepting branch is enough, so explicit enumeration of every branch is unnecessary. Therefore the statement is false.
Depends on
Used by
Dependency tree · two levels
9 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
- MIT 18.404J / 6.840J, Lecture 16: Cook-Levin Theorem (standard reference, not scraped)