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1½-Player Stochastic StopWatch Games

Author Sparsa Roychowdhury

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Sparsa Roychowdhury
  • Indian Institute of Technology Bombay, Mumbai, India


The author thanks Prof. Krishna S. of IIT Bombay, India for insightful discussions, suggestions and encouragement towards this work. The open access publication of this article was supported by the Alpen-Adria-Universität Klagenfurt, Austria.

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Sparsa Roychowdhury. 1½-Player Stochastic StopWatch Games. In 28th International Symposium on Temporal Representation and Reasoning (TIME 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 206, pp. 17:1-17:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


Stochastic timed games (STGs), introduced by Bouyer and Forejt, generalize continuous-time Markov chains and timed automata. Depending on the number of players - 2, 1, or 0 - subclasses of stochastic timed games are classified as 2½-player, 1½-player, and ½-player games where the ½ symbolizes the presence of the stochastic player. The qualitative and quantitative reachability problem for STGs was studied in [Patricia Bouyer and Vojtech Forejt, 2009] and [S. Akshay et al., 2016]. In this paper, we introduce stochastic stopwatch games (SSG), an extension of (STG) from clocks to stopwatches. We focus on 1½-player SSGs and prove that with two variables which can be either a clock or a stopwatch, qualitative reachability is decidable, whereas, if we increase the number of variables to three, with at least one stopwatch, the problem becomes undecidable.

Subject Classification

ACM Subject Classification
  • Theory of computation → Timed and hybrid models
  • Timed Automata
  • Stopwatches
  • Stochastic Timed Games


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