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Boolean Automata and Atoms of Regular Languages

Author Hellis Tamm

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LIPIcs.MFCS.2021.86.pdf
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Hellis Tamm
  • Department of Software Science, Tallinn University of Technology, Estonia

Funding

This work was supported by the Estonian Ministry of Education and Research grant IUT33-13 and by the Estonian Research Council grant PRG1210.

Acknowledgements

The author is indebted to late Janusz Brzozowski for suggesting the topic and for collaboration during the early stages of this work.

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Hellis Tamm. Boolean Automata and Atoms of Regular Languages. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 86:1-86:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.86

Abstract

We examine the role that atoms of regular languages play in boolean automata. We observe that the size of a minimal boolean automaton of a regular language is directly related to the number of atoms of the language. We present a method to construct minimal boolean automata, using the atoms of a given regular language. The "illegal" cover problem of the Kameda-Weiner method for NFA minimization implies that using the union operation only to construct an automaton from a cover - as is the case with NFAs -, is not sufficient. We show that by using the union and the intersection operations (without the complementation operation), it is possible to construct boolean automata accepting a given language, for a given maximal cover.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Boolean automaton
  • Regular language
  • Atoms

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