# Partial Solvers for Generalized Parity Games

## TL;DR

This paper introduces an extension of partial solvers for generalized parity games, combining them with Zielonka's recursive algorithm, and evaluates their performance on benchmark sets from the LTL synthesis competition.

## Contribution

It extends partial solvers to generalized parity games and integrates them with Zielonka's recursive algorithm, enhancing solving capabilities for complex game objectives.

## Key findings

- Partial solvers efficiently solve most benchmark games.
- Combined algorithms outperform classical methods in certain cases.
- Extended solvers handle conjunctions of parity objectives effectively.

## 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.