Branching-time Model Checking of One-counter Processes

Authors Stefan Göller, Markus Lohrey

Thumbnail PDF


  • Filesize: 150 kB
  • 12 pages

Document Identifiers

Author Details

Stefan Göller
Markus Lohrey

Cite AsGet BibTex

Stefan Göller and Markus Lohrey. Branching-time Model Checking of One-counter Processes. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 405-416, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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.
  • Model checking
  • computation tree logic
  • complexity theory


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads