English

Deciding minimal distinguishing DFAs is NP-complete

Formal Languages and Automata Theory 2023-06-07 v1

Abstract

In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language which is a subset of exactly one of the given languages. We establish the NP-hardness of this decision problem by providing a reduction from the Boolean Satisfiability Problem (SAT) to deciding the existence of a distinguishing automaton of a specific size.

Keywords

Cite

@article{arxiv.2306.03533,
  title  = {Deciding minimal distinguishing DFAs is NP-complete},
  author = {Jan Martens},
  journal= {arXiv preprint arXiv:2306.03533},
  year   = {2023}
}
R2 v1 2026-06-28T10:57:36.834Z