License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2018.30
URN: urn:nbn:de:0030-drops-85079
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8507/
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Fleischer, Lukas ; Kufleitner, Manfred

The Intersection Problem for Finite Monoids

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LIPIcs-STACS-2018-30.pdf (0.6 MB)

Abstract

We investigate the intersection problem for finite monoids, which asks for a given set of regular languages, represented by recognizing morphisms to finite monoids from a variety V, whether there exists a word contained in their intersection. Our main result is that the problem is PSPACE-complete if V is contained in DS and NP-complete if V is non-trivial and contained in DO. Our NP-algorithm for the case that V is contained in DO uses novel methods, based on compression techniques and combinatorial properties of DO. We also show that the problem is log-space reducible to the intersection problem for deterministic finite automata (DFA) and that a variant of the problem is log-space reducible to the membership problem for transformation monoids. In light of these reductions, our hardness results can be seen as a generalization of both a classical result by Kozen and a theorem by Beaudry, McKenzie and Thérien.

BibTeX - Entry

@InProceedings{fleischer_et_al:LIPIcs:2018:8507,
  author =	{Lukas Fleischer and Manfred Kufleitner},
  title =	{{The Intersection Problem for Finite Monoids}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{30:1--30:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8507},
  URN =		{urn:nbn:de:0030-drops-85079},
  doi =		{10.4230/LIPIcs.STACS.2018.30},
  annote =	{Keywords: intersection problem, finite monoid, recognizing morphism, complexity}
}

Keywords: intersection problem, finite monoid, recognizing morphism, complexity
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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