Temporal logic control of POMDPs via label-based stochastic simulation relations

The synthesis of controllers guaranteeing linear temporal logic specifications on partially observable Markov decision processes (POMDP) via their belief models causes computational issues due to the continuous spaces. In this work, we construct a finite-state abstraction on which a control policy is synthesized and refined back to the original belief model. We introduce a new notion of label-based approximate stochastic simulation to quantify the deviation between belief models. We develop a robust synthesis methodology that yields a lower bound on the satisfaction probability, by compensating for deviations a priori, and that utilizes a less conservative control refinement.