Partial Solvers for Generalized Parity Games

Abstract

Parity games have been broadly studied in recent years for their applications to controller synthesis and verification. In practice, partial solvers for parity games that execute in polynomial time, while incomplete, can solve most games in publicly available benchmark suites. In this paper, we combine those partial solvers with the classical recursive algorithm for parity games due to Zielonka. We also extend partial solvers to generalized parity games that are games with conjunction of parity objectives. We have implemented those algorithms and evaluated them on a large set of benchmarks proposed in the last LTL synthesis competition.

The Reactive Synthesis Competition (SYNTCOMP): 2018-2021

“…The input LTL formula is first decomposed into a conjunction of sub-formulas, which are in turn translated into deterministic parity automata, composed into a synchronised (generalized parity) product automaton, and finally translated into a generalized parity game using the tlsf2gpg 3 tool. The game is then solved using a combination of the recursive algorithm for generalized parity games (Chatterjee et al, 2007) and incomplete polynomial-time algorithms, called partial solvers, presented in Bruyère et al (2019). SPORE contains an explicit and a symbolic implementation of those algorithms, the latter relying on Binary Decision Diagrams (BDDs) to represent the game arena.…”

The Extended HOA Format for Synthesis

“…The hoa2pg tool 3 is a simplified version of one of the components present in a prototype synthesis tool which translates linear temporal logic into a parallel composition of several parity games [12]. In essence, it translate an extended-HOA automaton into a parity game using binary decision diagrams to abstract the atomic-proposition valuations labelling the transitions of the original automaton and by adding intermediate vertices representing the choices of the environment.…”