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Limit Synchronization in Markov Decision Processes

  • Laurent Doyen
  • Thierry Massart
  • Mahsa Shirmohammadi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8412)

Abstract

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing if the probability mass accumulates in a single state, possibly in the limit. Precisely, for 0 ≤ p ≤ 1 the sequence is p-synchronizing if a probability distribution in the sequence assigns probability at least p to some state, and we distinguish three synchronization modes: (i) sure winning if there exists a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there exists a strategy that produces a sequence that is, for all ε > 0, a (1-ε)-synchronizing sequence; (iii) limit-sure winning if for all ε > 0, there exists a strategy that produces a (1-ε)-synchronizing sequence. We consider the problem of deciding whether an MDP is sure, almost-sure, or limit-sure winning, and we establish the decidability and optimal complexity for all modes, as well as the memory requirements for winning strategies. Our main contributions are as follows: (a) for each winning modes we present characterizations that give a PSPACE complexity for the decision problems, and we establish matching PSPACE lower bounds; (b) we show that for sure winning strategies, exponential memory is sufficient and may be necessary, and that in general infinite memory is necessary for almost-sure winning, and unbounded memory is necessary for limit-sure winning; (c) along with our results, we establish new complexity results for alternating finite automata over a one-letter alphabet.

Keywords

Markov Decision Process Membership Problem Winning Region Probabilistic Automaton Emptiness Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Laurent Doyen
    • 1
  • Thierry Massart
    • 2
  • Mahsa Shirmohammadi
    • 1
    • 2
  1. 1.LSVENS Cachan & CNRSFrance
  2. 2.Université Libre de BruxellesBelgium

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