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DOI: 10.4230/LIPIcs.STACS.2010.2472
URN: urn:nbn:de:0030-drops-24722
URL: http://drops.dagstuhl.de/opus/volltexte/2010/2472/
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Göller, Stefan ; Lohrey, Markus

Branching-time Model Checking of One-counter Processes

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Abstract

One-counter processes (OCPs) are pushdown processes which operate only on a unary stack alphabet. We study the computational complexity of model checking computation tree logic ($\CTL$) over OCPs. A $\PSPACE$ upper bound is inherited from the modal $\mu$-calculus for this problem. First, we analyze the periodic behaviour of $\CTL$ over OCPs and derive a model checking algorithm whose running time is exponential only in the number of control locations and a syntactic notion of the formula that we call leftward until depth. Thus, model checking fixed OCPs against $\CTL$ formulas with a fixed leftward until depth is in $\P$. This generalizes a result of the first author, Mayr, and To for the expression complexity of $\CTL$'s fragment $\EF$. Second, we prove that already over some fixed OCP, $\CTL$ model checking is $\PSPACE$-hard. Third, we show that there already exists a fixed $\CTL$ formula for which model checking of OCPs is $\PSPACE$-hard. For the latter, we employ two results from complexity theory: (i) Converting a natural number in Chinese remainder presentation into binary presentation is in logspace-uniform $\NC^1$ and (ii) $\PSPACE$ is $\AC^0$-serializable. We demonstrate that our approach can be used to answer further open questions.

BibTeX - Entry

@InProceedings{gller_et_al:LIPIcs:2010:2472,
  author =	{Stefan G{\"o}ller and Markus Lohrey},
  title =	{{Branching-time Model Checking of One-counter Processes}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{405--416},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2472},
  URN =		{urn:nbn:de:0030-drops-24722},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2472},
  annote =	{Keywords: Model checking, computation tree logic, complexity theory}
}

Keywords: Model checking, computation tree logic, complexity theory
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2010
Date of publication: 09.03.2010


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