Solving Infinite-State Games via Acceleration (Full Version)

TL;DR

This paper introduces a novel acceleration technique for fixpoint algorithms to solve infinite-state games more efficiently, avoiding divergence and outperforming existing methods on benchmarks.

Contribution

It presents the first acceleration-based semi-algorithm for solving infinite-state games, improving convergence and efficiency over classical methods.

Findings

Outperforms state-of-the-art techniques on benchmarks

Can achieve convergence where existing algorithms diverge

First method to incorporate acceleration in infinite-state game solving

Abstract

Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to significant attention towards developing techniques for solving infinite-state games. We propose novel symbolic semi-algorithms for solving infinite-state games with temporal winning conditions. The novelty of our approach lies in the introduction of an acceleration technique that enhances fixpoint-based game-solving methods and helps to avoid divergence. Classical fixpoint-based algorithms, when applied to infinite-state games, are bound to diverge in many cases, since they iteratively compute the set of states from which one player has a winning strategy. Our proposed approach can lead to convergence in cases where existing algorithms require an infinite number of iterations. This is achieved by acceleration: computing an infinite set of states from which a simpler sub-strategy can be iterated an unbounded number of times in order to win the game. Ours is the first method for solving infinite-state games to employ acceleration. Thanks to this, it is able to outperform state-of-the-art techniques on a range of benchmarks, as evidenced by our evaluation of a prototype implementation.