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Decision Problems for Subregular Classes

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Implementation and Application of Automata (CIAA 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15015))

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Abstract

We study the computational complexity of deciding whether a given deterministic or nondeterministic finite automaton (DFA or NFA) recognizes a language in a given subclass of regular languages. We prove NL-completeness of this problem on both automata models for the classes of comma-free codes, solid codes, and singleton languages. For the classes of combinational, finitely generated left ideal, star, comet, group, and co-finite languages, the membership problem is NL-complete on DFAs and PSPACE-complete on NFAs. We also show that the membership problem on NFAs is NL-complete for the classes of prefix-, suffix-, factor-, and subword-free, singletons, and finite languages and it is PSPACE-hard for symmetric definite languages. Next, we show that deciding whether a given unary partial DFA recognizes an ordered language is L-complete and deciding whether a partial DFA can be ordered is NP-complete. Finally, deciding whether a given DFA (NFA) recognizes an ordered or power-separating language is NL-hard (PSPACE-hard, respectively).

M. Hospodár—This publication was supported by the Operational Programme Integrated Infrastructure (OPII) for the project 313011BWH2: “InoCHF – Research and development in the field of innovative technologies in the management of patients with CHF”, co-financed by the European Regional Development Fund.

V. Olejár—Parts of this work were conducted during the Erasmus+ mobility program with mobility ID 1409624.

J. Šebej–This research is funded by Slovak Research and Development Agency project under contract No. APVV-21-0336 “Analysis of Judicial Decisions using Artificial Intelligence”.

Supported by Slovak Grant Agency for Science (VEGA) under contract 2/0096/23 “Automata and Formal Languages: Descriptional and Computational Complexity”.

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Acknowledgments

We express our gratitude to the anonymous referees for their careful reading and useful suggestions for this paper. We also thank Galina Jirásková for fruitful discussions on the topic.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Michal Hospodár & Viktor Olejár

  2. Department of Computer Science, P. J. Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Viktor Olejár & Juraj Šebej

Authors
  1. Michal Hospodár
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  2. Viktor Olejár
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  3. Juraj Šebej
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Correspondence to Michal Hospodár .

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  1. Akita University, Akita, Japan

    Szilárd Zsolt Fazekas

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Hospodár, M., Olejár, V., Šebej, J. (2024). Decision Problems for Subregular Classes. In: Fazekas, S.Z. (eds) Implementation and Application of Automata. CIAA 2024. Lecture Notes in Computer Science, vol 15015. Springer, Cham. https://doi.org/10.1007/978-3-031-71112-1_13

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  • DOI: https://doi.org/10.1007/978-3-031-71112-1_13

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