Playing Safe

Authors Thomas Colcombet, Nathanael Fijalkow, Florian Horn

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Thomas Colcombet
Nathanael Fijalkow
Florian Horn

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Thomas Colcombet, Nathanael Fijalkow, and Florian Horn. Playing Safe. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 379-390, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)


We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety conditions. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety condition is given by the size of the maximal antichain of left quotients with respect to language inclusion. This result holds for all safety conditions without any regularity assumptions, and for all (finite or infinite) graphs of finite degree. We give several applications of this general principle. In particular, we characterize the exact memory requirements for the opponent in generalized reachability games, and we prove the existence of positional strategies in games with counters.
  • Game Theory
  • Synthesis
  • Safety Specifications
  • Program Verification


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