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arXiv · 2408.01212

Markov Decision Processes with Sure Parity and Multiple Reachability Objectives

Raphaël Berthon·Joost-Pieter Katoen·Tobias Winkler
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Abstract

This paper considers the problem of finding strategies that satisfy a mixture of sure and threshold objectives in Markov decision processes. We focus on a single $\omega$-regular objective expressed as parity that must be surely met while satisfying $n$ reachability objectives towards sink states with some probability thresholds too. We consider three variants of the problem: (a) strict and (b) non-strict thresholds on all reachability objectives, and (c) maximizing the thresholds with respect to a lexicographic order. We show that (a) and (c) can be reduced to solving parity games, and (b) can be solved in $\sf{EXPTIME}$. Strategy complexities as well as algorithms are provided for all cases.

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Raphaël Berthon, Joost-Pieter Katoen, Tobias Winkler. 2024-08-02. Markov Decision Processes with Sure Parity and Multiple Reachability Objectives. https://arxiv.org/abs/2408.01212

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