Model Checking for Probabilistic Multiagent Systems

Abstract

In multiagent systems, agents usually do not have complete information of the whole system, which makes the analysis of such systems hard. The incompleteness of information is normally modelled by means of accessibility relations, and the schedulers consistent with such relations are called uniform. In this paper, we consider probabilistic multiagent systems with accessibility relations and focus on the model checking problem with respect to the probabilistic epistemic temporal logic, which can specify both temporal and epistemic properties. However, the problem is undecidable in general. We show that it becomes decidable when restricted to memoryless uniform schedulers. Then, we present two algorithms for this case: one reduces the model checking problem into a mixed integer non-linear programming (MINLP) problem, which can then be solved by Satisfiability Modulo Theories (SMT) solvers, and the other is an approximate algorithm based on the upper confidence bounds applied to trees (UCT) algorithm, which can return a result whenever queried. These algorithms have been implemented in an existing model checker and then validated on experiments. The experimental results show the efficiency and extendability of these algorithms, and the algorithm based on UCT outperforms the one based on MINLP in most cases.