An Algorithm for Probabilistic Alternating Simulation

TL;DR

This paper introduces a polynomial-time algorithm for computing the largest probabilistic alternating simulation in probabilistic game structures, extending existing methods to handle mixed strategies efficiently.

Contribution

It presents the first polynomial-time partition-based algorithm for PA-simulation, expanding the GCPP framework to probabilistic game settings with mixed strategies.

Findings

Algorithm computes the largest PA-simulation efficiently.

Extends GCPP to probabilistic game structures with mixed strategies.

Improves upon previous methods for probabilistic simulation with mixed actions.

Abstract

In probabilistic game structures, probabilistic alternating simulation (PA-simulation) relations preserve formulas defined in probabilistic alternating-time temporal logic with respect to the behaviour of a subset of players. We propose a partition based algorithm for computing the largest PA-simulation, which is to our knowledge the first such algorithm that works in polynomial time, by extending the generalised coarsest partition problem (GCPP) in a game-based setting with mixed strategies. The algorithm has higher complexities than those in the literature for non-probabilistic simulation and probabilistic simulation without mixed actions, but slightly improves the existing result for computing probabilistic simulation with respect to mixed actions.