Interplays of Sure, Almost-Sure, and Threshold Parity Objectives on Markov Decision Processes

Two major approaches in synthesis consist in specifying either the worst case behaviour or specifying the stochastic behaviour of a system. This thesis aims at studying the interplays of sure and stochastic conditions by considering algorithms to decide the existence of strategies in Markov decision processes for combinations of objectives. These objectives are omega-regular properties expressed as parity conditions, that need to be enforced either surely, almost surely, or with some threshold probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms and complexity bounds for three main problems. First, we study multiple sure objectives, and multiple almost-sure objectives. Second, we consider Boolean combinations of sure objectives and multiple almost-sure objectives. Third, we consider one sure objective, and stochastic objectives that have to hold with a given probability threshold.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished