Parity Games Played on Transition Graphs of One-Counter Processes

  • Olivier Serre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3921)


We consider parity games played on special pushdown graphs, namely those generated by one-counter processes. For parity games on pushdown graphs, it is known from [23] that deciding the winner is an ExpTime-complete problem. An important corollary of this result is that the μ-calculus model checking problem for pushdown processes is ExpTime-complete. As one-counter processes are special cases of pushdown processes, it follows that deciding the winner in a parity game played on the transition graph of a one-counter process can be achieved in ExpTime. Nevertheless the proof for the ExpTime-hardness lower bound of [23] cannot be adapted to that case. Therefore, a natural question is whether the ExpTime upper bound can be improved in this special case. In this paper, we adapt techniques from [11,4] and provide a PSpace upper bound and a DP-hard lower bound for this problem. We also give two important consequences of this result. First, we improve the best upper bound known for model-checking one-counter processes against μ-calculus. Second, we show how these games can be used to solve pushdown games with winning conditions that are Boolean combinations of a parity condition on the control states with conditions on the stack height.


Model Check Turing Machine Conjunctive Normal Form Transition Graph Winning Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Olivier Serre
    • 1
  1. 1.LIAFAFrance

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