Parity Objectives in Countable MDPs

Kiefer, Stefan, Mayr, Richard, Shirmohammadi, Mahsa and Wojtczak, Dominik ORCID: 0000-0001-5560-0546 (2017) Parity Objectives in Countable MDPs. In: 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2017-6-20 - 2017-6-23.

Text main.pdf - Author Accepted Manuscript Download (332kB)

Abstract

We study countably infinite MDPs with parity objectives, and special cases with a bounded number of colors in the Mostowski hierarchy (including reachability, safety, Büchi and co-Büchi). 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., c-optimal) strategies for all objectives in the Mostowski hierarchy. In particular, there is a strong dichotomy between two different types of objectives. For the first type, optimal strategies, if they exist, can be chosen MD, while for the second type optimal strategies require infinite memory. (I.e., for all objectives in the Mostowski hierarchy, if finite-memory randomized strategies suffice then also MD-strategies suffice.) Similarly, some objectives admit c-optimal MD-strategies, while for others c-optimal strategies require infinite memory. Such a dichotomy also holds for the subclass of countably infinite MDPs that are finitely branching, though more objectives admit MD-strategies here.

Item Type:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	countable MDPs, parity objectives, strategies, memory requirement
Depositing User:	Symplectic Admin
Date Deposited:	31 May 2017 09:26
Last Modified:	15 Mar 2024 00:25
DOI:	10.1109/LICS.2017.8005100
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3007709