The complexity of stochastic M¨¹ller games
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- 作者：Krishnendu Chatterjee krish.chat@gmail.com krish.chat@ist.ac.at
- 关键词：Game theory ; Stochastic games ; Mü ; ller objectives ; ¦Ø-regular objectives
- 刊名：Information and Computation
- 出版年：2012
- 出版时间：February 2012
- 年：2012
- 卷：211
- 期：Complete
- 页码：29-48
- 全文大小：356 K
文摘
The theory of graph games with ¦Ø-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph games: the qualitative problem asks for the set of states from which a player can win with probability 1 (almost-sure winning); and the quantitative problem asks for the maximal probability of winning (optimal winning) from each state. We consider ¦Ø-regular winning conditions formalized as M¨¹ller winning conditions. We present optimal memory bounds for pure (deterministic) almost-sure winning and optimal winning strategies in stochastic graph games with M¨¹ller winning conditions. We also study the complexity of stochastic M¨¹ller games and show that both the qualitative and quantitative analysis problems are PSPACE-complete. Our results are relevant in synthesis of stochastic reactive processes.