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.FSTTCS.2017.12
URN: urn:nbn:de:0030-drops-84083
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8408/
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Bednarczyk, Bartosz ; Charatonik, Witold

Modulo Counting on Words and Trees

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LIPIcs-FSTTCS-2017-12.pdf (0.6 MB)

Abstract

We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a technique for deciding the satisfiability problem. In the case of words this gives a new proof of EXPSPACE upper bound, and in the case of trees it gives a 2EXPTIME algorithm. This algorithm is optimal: we prove a matching lower bound by a generic reduction from alternating Turing machines working in exponential space; the reduction involves a development of a new version of tiling games.

BibTeX - Entry

@InProceedings{bednarczyk_et_al:LIPIcs:2018:8408,
  author =	{Bartosz Bednarczyk and Witold Charatonik},
  title =	{{Modulo Counting on Words and Trees}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8408},
  URN =		{urn:nbn:de:0030-drops-84083},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.12},
  annote =	{Keywords: satisfiability, trees, words, two-variable logic, modulo quantifiers}
}

Keywords: satisfiability, trees, words, two-variable logic, modulo quantifiers
Collection: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 12.02.2018

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