On-The-Fly Solving for Symbolic Parity Games

TL;DR

This paper introduces on-the-fly solving methods for incomplete symbolic parity games, enabling efficient decision-making for specific vertices during exploration, with practical implementation demonstrating significant speed-ups.

Contribution

It formalizes on-the-fly and partial solving techniques for incomplete parity games, enhancing efficiency and resilience during game exploration.

Findings

Speed-ups of several orders of magnitude achieved

Low overhead in practical implementations

Effective decision-making for designated vertices

Abstract

Parity games can be used to represent many different kinds of decision problems. In practice, tools that use parity games often rely on a specification in a higher-order logic from which the actual game can be obtained by means of an exploration. For many of these decision problems we are only interested in the solution for a designated vertex in the game. We formalise how to use on-the-fly solving techniques during the exploration process, and show that this can help to decide the winner of such a designated vertex in an incomplete game. Furthermore, we define partial solving techniques for incomplete parity games and show how these can be made resilient to work directly on the incomplete game, rather than on a set of safe vertices. We implement our techniques for symbolic parity games and study their effectiveness in practice, showing that speed-ups of several orders of magnitude are feasible and overhead (if unavoidable) is typically low.