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Minimization of Deterministic Finite Automata Modulo the Edit Distance

Authors Jakub Michaliszyn , Jan Otop

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ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • automata theory
  • automata minimization
  • edit distance

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Abstract

We propose a novel approach to minimization of deterministic finite automata (DFA), in which the DFA is further minimized at the expense of relaxing equality of languages to merely a similarity. As the notion of similarity of languages, we consider the edit distance between languages ℒ, ℒ', i.e., the minimal number of edits necessary to transform any word from ℒ to some word from ℒ' and vice versa.
In this paper we address two problems: minimization up to a predetermined edit distance given in the input, and minimization up to a bounded edit distance, in which there has to be an upper bound on the number of edits, but it is not specified. We show the first problem to be PSpace {}-complete and that the second problem is in Σ₂^p, and both NP-hard and coNP-hard. We show that if we limit how many strongly connected components can be visited by a single run (i.e., bounded SCC-depth), the problem becomes NP-complete. We also establish maximal subclasses of DFA over which minimization up to a bounded edit distance can be performed in polynomial time. 
Additionally, we provide a succinct overview of alternative metrics for assessing language similarity.

Cite As Get BibTex

Jakub Michaliszyn and Jan Otop. Minimization of Deterministic Finite Automata Modulo the Edit Distance. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 77:1-77:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.MFCS.2025.77

Author Details

Jakub Michaliszyn
  • University of Wrocław, Poland
Jan Otop
  • University of Wrocław, Poland

Funding

This work was supported by the National Science Centre (NCN), Poland under grant 2020/39/B/ST6/00521.

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