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We give polynomial-time algorithms for computing the values of Markovdecision processes (MDPs) with limsup and liminf objectives. A real-valuedreward is assigned to each state, and the value of an infinite path in the MDPis the limsup (resp. liminf) of all rewards along the path. The value of an MDPis the maximal expected value of an infinite path that can be achieved byresolving the decisions of the MDP. Using our result on MDPs, we show thatturn-based stochastic games with limsup and liminf objectives can be solved inNP \cap coNP.

Probabilistic Systems with LimSup and LimInf Objectives