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International Conference on Formal Modeling and Analysis of Timed Systems

FORMATS 2019: Formal Modeling and Analysis of Timed Systems pp 282–300Cite as

Expected Reachability-Price Games

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11750))

Abstract

Probabilistic timed automata(PTA) model real-time systems with non-deterministic and stochastic behavior. They extend Alur-Dill timed automata by allowing probabilistic transitions and a price structure on the locations and transitions. Thus, a PTA can be considered as a Markov decision process (MDP) with uncountably many states and transitions. Expected reachability-price games are turn-based games where two players, player \(\text {Min}\) and player \(\text {Max}\), move a token along the infinite configuration space of PTA. The objective of player \(\text {Min}\) is to minimize the expected price to reach a target location, while the goal of the \(\text {Max}\) player is the opposite. The undecidability of computing the value in the expected reachability-price games follows from the undecidability of the corresponding problem on timed automata. A key contribution of this work is a characterization of sufficient conditions under which an expected reachability-price game can be reduced to a stochastic game on a stochastic generalization of corner-point abstraction (a well-known finitary abstraction of timed automata). Exploiting this result, we show that expected reachability-price games for PTA with single clock and price-rates restricted to \(\{ 0, 1 \}\) are decidable.

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Authors and Affiliations

  1. Université libre de Bruxelles, Brussels, Belgium

    Shibashis Guha

  2. University of Colorado Boulder, Boulder, USA

    Ashutosh Trivedi

Authors
  1. Shibashis Guha
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  2. Ashutosh Trivedi
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Correspondence to Shibashis Guha .

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Editors and Affiliations

  1. Université Paris 13, Villetaneuse, France

    Étienne André

  2. University of Twente, Enschede, The Netherlands

    Mariëlle Stoelinga

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Guha, S., Trivedi, A. (2019). Expected Reachability-Price Games. In: André, É., Stoelinga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2019. Lecture Notes in Computer Science(), vol 11750. Springer, Cham. https://doi.org/10.1007/978-3-030-29662-9_17

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  • DOI: https://doi.org/10.1007/978-3-030-29662-9_17

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  • Online ISBN: 978-3-030-29662-9

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