License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.86
URN: urn:nbn:de:0030-drops-145267
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14526/
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Tamm, Hellis

Boolean Automata and Atoms of Regular Languages

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LIPIcs-MFCS-2021-86.pdf (0.5 MB)


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.

BibTeX - Entry

@InProceedings{tamm:LIPIcs.MFCS.2021.86,
  author =	{Tamm, Hellis},
  title =	{{Boolean Automata and Atoms of Regular Languages}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{86:1--86:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14526},
  URN =		{urn:nbn:de:0030-drops-145267},
  doi =		{10.4230/LIPIcs.MFCS.2021.86},
  annote =	{Keywords: Boolean automaton, Regular language, Atoms}
}

Keywords: Boolean automaton, Regular language, Atoms
Collection: 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)
Issue Date: 2021
Date of publication: 18.08.2021


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