Probabilistic Systems with LimSup and LimInf Objectives

Authors:
Krishnendu Chatterjee;Thomas A. Henzinger
Affiliations:
Jack Baskin School of Engineering, University of California at Santa Cruz, Santa Cruz, United States of America 95064;School of Computer and Communication Sciences, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland 1015
Venue:
Infinity in Logic and Computation
Year:
2009

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Abstract

We give polynomial-time algorithms for computing the values of Markov decision processes (MDPs) with limsup and liminf objectives. A real-valued reward is assigned to each state, and the value of an infinite path in the MDP is the limsup (resp. liminf) of all rewards along the path. The value of an MDP is the maximal expected value of an infinite path that can be achieved by resolving the decisions of the MDP. Using our result on MDPs, we show that turn-based stochastic games with limsup and liminf objectives can be solved in NP 驴 coNP.