License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.MFCS.2016.67
URN: urn:nbn:de:0030-drops-64799
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6479/
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Masopust, Tomás

Piecewise Testable Languages and Nondeterministic Automata

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Abstract

A regular language is k-piecewise testable if it is a finite boolean combination of languages of the form Sigma^* a_1 Sigma^* ... Sigma^* a_n Sigma^*, where a_i in Sigma and 0 <= n <= k. Given a DFA A and k >= 0, it is an NL-complete problem to decide whether the language L(A) is piecewise testable and, for k >= 4, it is coNP-complete to decide whether the language L(A) is k-piecewise testable. It is known that the depth of the minimal DFA serves as an upper bound on k. Namely, if L(A) is piecewise testable, then it is k-piecewise testable for k equal to the depth of A. In this paper, we show that some form of nondeterminism does not violate this upper bound result. Specifically, we define a class of NFAs, called ptNFAs, that recognize piecewise testable languages and show that the depth of a ptNFA provides an (up to exponentially better) upper bound on k than the minimal DFA. We provide an application of our result, discuss the relationship between k-piecewise testability and the depth of NFAs, and study the complexity of k-piecewise testability for ptNFAs.

BibTeX - Entry

@InProceedings{masopust:LIPIcs:2016:6479,
  author =	{Tom{\'a}s Masopust},
  title =	{{Piecewise Testable Languages and Nondeterministic Automata}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{67:1--67:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6479},
  URN =		{urn:nbn:de:0030-drops-64799},
  doi =		{10.4230/LIPIcs.MFCS.2016.67},
  annote =	{Keywords: automata, logics, languages, k-piecewise testability, nondeterminism}
}

Keywords: automata, logics, languages, k-piecewise testability, nondeterminism
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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