A Delayed Promotion Policy for Parity Games

TL;DR

This paper introduces a delayed promotion technique for solving parity games that improves efficiency and potentially avoids exponential worst-case scenarios, enhancing the practical applicability of dominion-based algorithms.

Contribution

It proposes a novel delayed promotion method for priority promotion in parity games, reducing exponential behaviors and improving performance over existing approaches.

Findings

Often outperforms original priority promotion method

No known exponential worst-case behavior so far

Improves practical efficiency in solving parity games

Abstract

Parity games are two-player infinite-duration games on graphs that play a crucial role in various fields of theoretical computer science. Finding efficient algorithms to solve these games in practice is widely acknowledged as a core problem in formal verification, as it leads to efficient solutions of the model-checking and satisfiability problems of expressive temporal logics, e.g., the modal muCalculus. Their solution can be reduced to the problem of identifying sets of positions of the game, called dominions, in each of which a player can force a win by remaining in the set forever. Recently, a novel technique to compute dominions, called priority promotion, has been proposed, which is based on the notions of quasi dominion, a relaxed form of dominion, and dominion space. The underlying framework is general enough to accommodate different instantiations of the solution procedure, whose correctness is ensured by the nature of the space itself. In this paper we propose a new such instantiation, called delayed promotion, that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case. The resulting procedure not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.