Tight Game Abstractions of Probabilistic Automata

  • Falak Sher Vira
  • Joost-Pieter Katoen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8704)


We present a new game-based abstraction technique for probabilistic automata (PA). The key idea is to use distribution-based abstraction – preserving novel distribution-based (alternating) simulation relations – rather than classical state-based abstraction. These abstractions yield (simple) probabilistic game automata (PGA), turn-based 2 player stochastic games in which moves of both players – as opposed to classical stochastic games – yield distributions over states. As distribution-based (alternating) simulation relations are pre-congruences for composite PGA, abstraction can be done compositionally. Our abstraction yields tighter upper and lower bounds on (extremal) reachability probabilities than state-based abstraction. This shows the potential superiority over state-based abstraction of PA and Markov decision processes.


Abstract Model Markov Decision Process Stochastic Game Concrete State Simulation Relation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Falak Sher Vira
    • 1
  • Joost-Pieter Katoen
    • 1
  1. 1.Software Modeling and VerificationRWTH Aachen UniversityAachenGermany

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