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.
A missing 1-transition shows the drawn machine is not yet a DFA
Statement refuted
The statement "a DFA transition diagram may omit a sink without changing totality" is false.
Facts & Assumptions
Given: The alphabet and the one-state picture with only the loop .
The statement refuted is: omitting a sink transition does not affect whether the diagram defines a DFA.
A DFA requires a total transition function on , by Deterministic finite automata.
Counterexample
The picture specifies a transition on input 0 but no transition on input 1. So the pair has no image.
By [L1], that means the picture does not define a DFA at all. Adding a sink state with a 1-edge repairs the omission, which is exactly why the original claim fails.
Therefore this one-state picture is a counterexample to [A1].
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
6 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)