Parity Objectives in Countable MDPs

We study countably infinite MDPs with parity objectives, and special cases with a bounded number of colors in the Mostowski hierarchy (including reachability, safety, Buchi and co-Buchi). In finite MDPs there always exist optimal memoryless deterministic (MD) strategies for parity objectives, but this does not generally hold for countably infinite MDPs. In particular, optimal strategies need not exist. For countable infinite MDPs, we provide a complete picture of the memory requirements of optimal (resp. , ϵ-optimal) strategies for all objectives in the Mostowski hierarchy. Extended abstract available in PDF.

Authors

• Dominik Wojtczak University of Liverpool

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