False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-12

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.

FALSE: epsilon is an input symbol

Statement

False claim: in an NFA with epsilon-moves, the symbol $ε$ is one more input symbol in the alphabet.

Facts & Assumptions

Given: An NFA with epsilon-moves over an alphabet $Σ$ .

[A1]

The statement refuted is: $ε$ is an input symbol of the machine.

[L1]

By Nondeterministic finite automata with epsilon-moves, the alphabet is $Σ$ , while $ε$ appears only in the transition domain $Σ \cup {ε}$ to denote a move that consumes no input symbol.

Refutation

technique · direct

1.1

The definition distinguishes the alphabet letters from $ε$ -moves: letters of $Σ$ are read from the input word, whereas an $ε$ -transition changes state without reading any letter.

L1given

2.1

So $ε$ is not part of the input alphabet itself. It is extra transition notation for "read nothing."

L1step 1.1

3.1

This contradicts [A1]. Therefore the claim is false.

A1step 2.1∎

Depends on

Nondeterministic finite automata with epsilon-moves

Used by

Nothing in the library uses this result yet.

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

Jean Gallier and Jocelyn Quaintance, Introduction to the Theory of Computation: Some Notes for CIS511 (standard reference, not scraped)