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.
One accepting branch is enough for an NFA to accept
Statement refuted
The statement "an NFA accepts a word only if every branch accepts" is false.
Facts & Assumptions
Given: The NFA and input word from FALSE: an NFA accepts only if every branch accepts.
The statement refuted is: an NFA accepts a word only if every branch accepts.
The false statement's refutation already exhibits one accepting branch and one rejecting branch on the same input, by FALSE: an NFA accepts only if every branch accepts.
Counterexample
On the input , one branch follows the path and accepts, while another branch stays on the start-state loop too long and rejects.
Therefore the same machine and the same word witness that acceptance can occur even when not every branch accepts.
This contradicts [A1], so the displayed NFA on is a counterexample.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
2 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
- Jean Gallier and Jocelyn Quaintance, Introduction to the Theory of Computation: Some Notes for CIS511 (standard reference, not scraped)