# Solving parity games via priority promotion

@article{Benerecetti2016SolvingPG,
title={Solving parity games via priority promotion},
author={Massimo Benerecetti and Daniele Dell'Erba and Fabio Mogavero},
journal={Formal Methods in System Design},
year={2016},
volume={52},
pages={193-226}
}
• Published 17 July 2016
• Computer Science
• Formal Methods in System Design
We consider parity games, a special form of two-player infinite-duration games on numerically labeled graphs, whose winning condition requires that the maximal value of a label occurring infinitely often during a play be of some specific parity. The problem of identifying the corresponding winning regions has a rather intriguing status from a complexity theoretic viewpoint, since it belongs to the class $${\textsc {UPTime}} \cap {\textsc {CoUPTime}}$$UPTIME∩COUPTIME, and still open is the…

### Improving Priority Promotion for Parity Games

• Computer Science
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• 2016
A new instantiation, called region recovery, is proposed that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case, and not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.

### A Delayed Promotion Policy for Parity Games

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A new instantiation, called delayed promotion, is proposed that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case, and not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.

### The priority promotion approach to parity games

• Computer Science
• 2017
A new family of algorithms is presented, based on the idea of promoting vertices to higher priorities during the search for winning regions, for the solution of parity games, exhibiting the best space complexity among the currently known solutions.

### BDD-based parity game solving

• Computer Science
• 2018
Zielonka’s BDD-based algorithm beats the B DD-based Priority Promotion algorithm by a small margin for games that are characteristic of practical veriﬁcation problems, and the Fixpoint-Iteration algorithm performs similar to Ziel onka‘s algorithm for games with at most 5 diﬀerent priorities.

### Solving Random Parity Games in Polynomial Time

• Computer Science
ArXiv
• 2020
It is proved that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a polynomial time algorithm that solves the game with high probability when the number of nodes goes to infinity.

### Improving parity games in practice

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This work deeply revisit the implementation of Zielonka’s recursive algorithm by dealing with the use of specific data structures and programming languages such as Scala, Java, C++, and Go, and shows that these choices are successful.

### Improved Set-based Symbolic Algorithms for Parity Games

• Computer Science
CSL
• 2017
This work presents two set-based symbolic algorithms for parity games that requires at most a sub-exponential number of symbolic operations and develops an algorithm that requires $O(n^{c/3+1})$ symbolic Operations and only linear space.

### Smaller progress measures and separating automata for parity games

• Computer Science
Frontiers in Computer Science
• 2022
This work suggests several adjustments to the approach of Calude et al. that lead to smaller statespaces, and identifies two that, together, lead to a statespace of exactly the same size Jurdzinski and Lazic's concise progress measures, which currently hold the crown as the smallest statespace.

### Exploring and implementing quasi-polynomial time algorithms for solving parity games

• Computer Science
• 2019
This document focuses on two quasi-polynomial parity game solvers – succinct progress measures by Jurdziński and Lazić and register games by Lehtinen and investigates both algorithms from a theoretical and practical perspective.

### Parity Games: Another View on Lehtinen's Algorithm

It is proved that the construction of the Lehtinen algorithm's separating automata actually leads to a faster algorithm than originally claimed in her paper: its complexity is $n^{O(\log n)}$ rather than $n(\log d \cdot \log n)$ (where $n$ is the number of nodes, and $d$the number of priorities of a considered parity game), which is similar to complexities of the other quasi-polynomial-time algorithms.

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