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DOI: 10.4230/LIPIcs.CSL.2015.441

A Unified Approach to Boundedness Properties in MSO

Authors: Lukasz Kaiser, Martin Lang, Simon Leßenich, and Christof Löding

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract

In the past years, extensions of monadic second-order logic (MSO) that can specify boundedness properties by the use of operators referring to the sizes of sets have been considered. In particular, the logics costMSO introduced by T. Colcombet and MSO+U by M. Bojanczyk were analyzed and connections to automaton models have been established to obtain decision procedures for these logics. In this work, we propose the logic quantitative counting MSO (qcMSO for short), which combines aspects from both costMSO and MSO+U. We show that both logics can be embedded into qcMSO in a natural way. Moreover, we provide a decidability proof for the theory of its weak variant (quantification only over finite sets) for the natural numbers with order and the infinite binary tree. These decidability results are obtained using a regular cost function extension of automatic structures called resource-automatic structures.

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Lukasz Kaiser, Martin Lang, Simon Leßenich, and Christof Löding. A Unified Approach to Boundedness Properties in MSO. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 441-456, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kaiser_et_al:LIPIcs.CSL.2015.441,
  author =	{Kaiser, Lukasz and Lang, Martin and Le{\ss}enich, Simon and L\"{o}ding, Christof},
  title =	{{A Unified Approach to Boundedness Properties in MSO}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{441--456},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.441},
  URN =		{urn:nbn:de:0030-drops-54309},
  doi =		{10.4230/LIPIcs.CSL.2015.441},
  annote =	{Keywords: quantitative logics, monadic second order logic, boundedness, automatic structures, tree automata}
}

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A Unified Approach to Boundedness Properties in MSO

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