Antichains for Concurrent Parameterized Games

TL;DR

This paper introduces a symbolic antichain-based method to efficiently compute winning strategies in concurrent parameterized games with an arbitrary number of players, improving decision procedures for reachability objectives.

Contribution

It presents two fixed-point algorithms using antichains to compute Eve's winning region, offering a more symbolic and potentially efficient approach.

Findings

Algorithms successfully implemented in C++

Antichain approach reduces complexity of knowledge game analysis

Experimental results show performance improvements on benchmarks

Abstract

Concurrent parameterized games involve a fixed yet arbitrary number of players. They are described by finite arenas in which the edges are labeled with languages that describe the possible move combinations leading from one vertex to another (n players yield a word of length n). Previous work showed that, when edge labels are regular languages, one can decide whether a distinguished player, called Eve, has a uniform strategy to ensure a reachability objective, against any strategy profile of her arbitrarily many opponents. This decision problem is known to be PSPACE-complete. A basic ingredient in the PSPACE algorithm is the reduction to the exponential-size knowledge game, a 2-player game that reflects the knowledge Eve has on the number of opponents. In this paper, we provide a symbolic approach, based on antichains, to compute Eve's winning region in the knowledge game. In words, it gives the minimal knowledge Eve needs at every vertex to win the concurrent parameterized reachability game. More precisely, we propose two fixed-point algorithms that compute, as an antichain, the maximal elements of the winning region for Eve in the knowledge game. We implemented in C++ these two algorithms, as well as the one initially proposed, and report on their relative performances on various benchmarks.