Equivalence of Games with Probabilistic Uncertainty and Partial-Observation Games

  • Krishnendu Chatterjee
  • Martin Chmelík
  • Rupak Majumdar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7561)


We introduce games with probabilistic uncertainty, a model for controller synthesis in which the controller observes the state through imprecise sensors that provide correct information about the current state with a fixed probability. That is, in each step, the sensors return an observed state, and given the observed state, there is a probability distribution (due to the estimation error) over the actual current state. The controller must base its decision on the observed state (rather than the actual current state, which it does not know). On the other hand, we assume that the environment can perfectly observe the current state. We show that controller synthesis for qualitative ω-regular objectives in our model can be reduced in polynomial time to standard partial-observation stochastic games, and vice-versa. As a consequence we establish the precise decidability frontier for the new class of games, and establish optimal complexity results for all the decidable problems.


Probability Measure Pure Strategy Markov Decision Process Stochastic Game Observation Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Martin Chmelík
    • 1
  • Rupak Majumdar
    • 2
  1. 1.IST Austria (Institute of Science and Technology Austria)Austria
  2. 2.MPI-SWSGermany

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