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Communication Dans Un Congrès Année : 2020

Strategy Complexity of Parity Objectives in Countable MDPs

Résumé

We study countably infinite MDPs with parity objectives. Unlike in finite MDPs, optimal strategies need not exist, and may require infinite memory if they do. We provide a complete picture of the exact strategy complexity of ε-optimal strategies (and optimal strategies, where they exist) for all subclasses of parity objectives in the Mostowski hierarchy. Either MD-strategies, Markov strategies, or 1-bit Markov strategies are necessary and sufficient, depending on the number of colors, the branching degree of the MDP, and whether one considers ε-optimal or optimal strategies. In particular, 1-bit Markov strategies are necessary and sufficient for ε-optimal (resp. optimal) strategies for general parity objectives.

Dates et versions

hal-03064654 , version 1 (14-12-2020)

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Stefan Kiefer, Richard Mayr, Mahsa Shirmohammadi, Patrick Totzke. Strategy Complexity of Parity Objectives in Countable MDPs. 31st International Conference on Concurrency Theory, CONCUR 2020, Aug 2020, Vienna, Austria. pp.39:1--39:17, ⟨10.4230/LIPIcs.CONCUR.2020.39⟩. ⟨hal-03064654⟩
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