Branching-Time Model Checking of Parametric One-Counter Automata

  • Stefan Göller
  • Christoph Haase
  • Joël Ouaknine
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)


We study the computational complexity of model checking EF logic and modal logic on parametric one-counter automata (POCA). A POCA is a one-counter automaton whose counter updates are either integer values encoded in binary or integer-valued parameters. Given a formula and a configuration of a POCA, the model-checking problem asks whether the formula is true in this configuration for all possible valuations of the parameters. We show that this problem is undecidable for EF logic via reduction from Hilbert’s tenth problem, however for modal logic we prove PSPACE-completeness. Obtaining the PSPACE upper bound involves analysing systems of linear Diophantine inequalities of exponential size that admit solutions of polynomial size. Finally, we show that model checking EF logic on POCA without parameters is PSPACE-complete.


Model Check Modal Logic Transition System Atomic Proposition Strongly Connect Component 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stefan Göller
    • 1
  • Christoph Haase
    • 2
  • Joël Ouaknine
    • 2
  • James Worrell
    • 2
  1. 1.Institut für InformatikUniversität BremenGermany
  2. 2.Department of Computer ScienceUniversity of OxfordUK

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