10.4230/LIPICS.STACS.2010.2472
Göller, Stefan
Stefan
Göller
Lohrey, Markus
Markus
Lohrey
Branching-time Model Checking of One-counter Processes
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
2010
Article
Model checking
computation tree logic
complexity theory
Marion, Jean-Yves
Jean-Yves
Marion
Schwentick, Thomas
Thomas
Schwentick
2010
2010-03-09
2010-03-09
2010-03-09
en
urn:nbn:de:0030-drops-24722
10.4230/LIPIcs.STACS.2010
978-3-939897-16-3
1868-8969
10.4230/LIPIcs.STACS.2010
LIPIcs, Volume 5, STACS 2010
27th International Symposium on Theoretical Aspects of Computer Science
2013
5
36
405
416
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Marion, Jean-Yves
Jean-Yves
Marion
Schwentick, Thomas
Thomas
Schwentick
1868-8969
Leibniz International Proceedings in Informatics (LIPIcs)
2010
5
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
12 pages
154032 bytes
application/pdf
Creative Commons Attribution-NoDerivs 3.0 Unported license
info:eu-repo/semantics/openAccess
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.
LIPIcs, Vol. 5, 27th International Symposium on Theoretical Aspects of Computer Science, pages 405-416