# Universal Algorithms for Parity Games and Nested Fixpoints

@inproceedings{Jurdzinski2020UniversalAF, title={Universal Algorithms for Parity Games and Nested Fixpoints}, author={Marcin Jurdzi'nski and R{\'e}mi Morvan and K. S. Thejaswini}, booktitle={Principles of Systems Design}, year={2020} }

A bstract An attractor decomposition meta-algorithm for solving parity games is given that general-ises the classic McNaughton-Zielonka algorithm and its recent quasi-polynomial variants due to Parys ( 2019 ), and to Lehtinen, Schewe, and Wojtczak ( 2019 ). The central concepts studied and exploited are attractor decompositions of dominia in parity games and the ordered trees that describe the inductive structure of attractor decompositions. The universal algorithm yields McNaughton-Zielonka…

## 2 Citations

### A Technique to Speed up Symmetric Attractor-Based Algorithms for Parity Games

- Computer ScienceFSTTCS
- 2022

This work pin-points the mechanism that is responsible for relative underperformance in the classic McNaughton-Zielonka algorithm, and proposes a new technique that eliminates it, based on enhancing the algorithm to compute attractor decompositions of subgames instead of just winning strategies on them.

### Operations on Fixpoint Equation Systems

- Mathematics, Computer ScienceArXiv
- 2023

This work studies operations on fixpoint equation systems (FES) over arbitrary complete lattices and investigates under which conditions these operations, such as substituting variables by their definition, preserve the solution of a FES.

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