@article{1477, abstract = {We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages provides a robust specification language to express properties in verification, and parity objectives are canonical forms to express them. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are undecidable even for special cases of parity objectives, we establish decidability (with optimal complexity) for POMDPs with all parity objectives under finite-memory strategies. We establish optimal (exponential) memory bounds and EXPTIME-completeness of the qualitative analysis problems under finite-memory strategies for POMDPs with parity objectives. We also present a practical approach, where we design heuristics to deal with the exponential complexity, and have applied our implementation on a number of POMDP examples.}, author = {Chatterjee, Krishnendu and Chmelik, Martin and Tracol, Mathieu}, journal = {Journal of Computer and System Sciences}, number = {5}, pages = {878 -- 911}, publisher = {Elsevier}, title = {{What is decidable about partially observable Markov decision processes with ω-regular objectives}}, doi = {10.1016/j.jcss.2016.02.009}, volume = {82}, year = {2016}, }