2016/09/13 by Massimo Benerecetti, Daniele Dell’Erba, Daniele Dell'Erba +1
Computer Science · Mathematics · #Algorithm #Computer science #Correctness #Discrete mathematics #Dominion #Formal Methods in Verification #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Model checking #Satisfiability #Theoretical computer science #cs.DS #cs.GT
paper · pdf · doi:10.4204/eptcs.226.3
published as EPTCS 226, 2016, pp. 30-45 · In Proceedings GandALF 2016, arXiv:1609.03648
openalex publication_date 2016/09/13 · arxiv created 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.