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DOI: 10.4230/LIPIcs.ICALP.2019.103
URN: urn:nbn:de:0030-drops-106790
URL: http://drops.dagstuhl.de/opus/volltexte/2019/10679/
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Barceló, Pablo ; Hong, Chih-Duo ; Le, Xuan-Bach ; Lin, Anthony W. ; Niskanen, Reino

Monadic Decomposability of Regular Relations

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Abstract

Monadic decomposibility - the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas - is a powerful tool for devising a decision procedure for a given logical theory. In this paper, we revisit a classical decision problem in automata theory: given a regular (a.k.a. synchronized rational) relation, determine whether it is recognizable, i.e., it has a monadic decomposition (that is, a representation as a boolean combination of cartesian products of regular languages). Regular relations are expressive formalisms which, using an appropriate string encoding, can capture relations definable in Presburger Arithmetic. In fact, their expressive power coincide with relations definable in a universal automatic structure; equivalently, those definable by finite set interpretations in WS1S (Weak Second Order Theory of One Successor). Determining whether a regular relation admits a recognizable relation was known to be decidable (and in exponential time for binary relations), but its precise complexity still hitherto remains open. Our main contribution is to fully settle the complexity of this decision problem by developing new techniques employing infinite Ramsey theory. The complexity for DFA (resp. NFA) representations of regular relations is shown to be NLOGSPACE-complete (resp. PSPACE-complete).

BibTeX - Entry

@InProceedings{barcel_et_al:LIPIcs:2019:10679,
  author =	{Pablo Barcel{\'o} and Chih-Duo Hong and Xuan-Bach Le and Anthony W. Lin and Reino Niskanen},
  title =	{{Monadic Decomposability of Regular Relations}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{103:1--103:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10679},
  URN =		{urn:nbn:de:0030-drops-106790},
  doi =		{10.4230/LIPIcs.ICALP.2019.103},
  annote =	{Keywords: Transducers, Automata, Synchronized Rational Relations, Ramsey Theory, Variable Independence, Automatic Structures}
}

Keywords: Transducers, Automata, Synchronized Rational Relations, Ramsey Theory, Variable Independence, Automatic Structures
Seminar: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 08.07.2019


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