Modal characterisation of simulation relations in probabilistic concurrent games

Abstract

Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation and bisimulation are important tools to compare the behaviour of different probabilistic game structures. In this paper, we present a sound and complete modal characterisation of these two relations by proposing a new modal logic based on probability distributions. This logic enables a player to enforce a property in the next state or distribution. We further extend the logic with fixpoint operators, which also characterises the simulation relations. This logic can express a lot of interesting properties in practical applications. • Modal characterization for Probabilistic Alternating Simulation (and Bisimulation). • A new modal logic for probability distributions in concurrent game structures. • Extends the modal logic with fixpoint operators.