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Related papers: Parity Games: Another View on Lehtinen's Algorithm

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This paper discusses the problem of efficiently solving parity games where player Odd has to obey an additional 'strong transition fairness constraint' on its vertices -- given that a player Odd vertex $v$ is visited infinitely often, a…

Computer Science and Game Theory · Computer Science 2023-10-24 Irmak Sağlam , Anne-Kathrin Schmuck

Parity games can be used to represent many different kinds of decision problems. In practice, tools that use parity games often rely on a specification in a higher-order logic from which the actual game can be obtained by means of an…

Logic in Computer Science · Computer Science 2022-01-25 Maurice Laveaux , Wieger Wesselink , Tim A. C. Willemse

We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions. We show that the integration of…

Logic in Computer Science · Computer Science 2019-07-16 Massimo Benerecetti , Daniele Dell'Erba , Fabio Mogavero

Recently Cristian S. Calude, Sanjay Jain, Bakhadyr Khoussainov, Wei Li and Frank Stephan proposed a quasi-polynomial time algorithm for parity games. This paper proposes a short proof of correctness of their algorithm.

Formal Languages and Automata Theory · Computer Science 2017-04-25 Hugo Gimbert , Rasmus Ibsen-Jensen

Open parity games are proposed as a compositional extension of parity games with algebraic operations, forming string diagrams of parity games. A potential application of string diagrams of parity games is to describe a large parity game…

Logic in Computer Science · Computer Science 2025-05-29 Kazuki Watanabe

We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are \emph{concurrent} in that at each turn, both players independently propose…

Logic in Computer Science · Computer Science 2019-03-14 Krishnendu Chatterjee , Thomas A. Henzinger , Vinayak S. Prabhu

We improve the complexity of solving parity games (with priorities in vertices) for $d={\omega}(\log n)$ by a factor of ${\theta}(d^2)$: the best complexity known to date was $O(mdn^{1.45+\log_2(d/\log_2(n))})$, while we obtain…

Computer Science and Game Theory · Computer Science 2023-05-02 Paweł Parys , Aleksander Wiącek

We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…

Quantum Physics · Physics 2021-07-05 Hyejung H. Jee , Carlo Sparaciari , Omar Fawzi , Mario Berta

This paper provides a polynomial-time algorithm for solving parity games that runs in $\mathcal{O}(n^{2}\cdot(n + m))$ time-ending a search that has taken decades. Unlike previous attractor-based algorithms, the presented algorithm only…

Data Structures and Algorithms · Computer Science 2025-11-07 Rick van der Heijden

The Strahler number of a rooted tree is the largest height of a perfect binary tree that is its minor. The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor…

Data Structures and Algorithms · Computer Science 2020-08-04 Laure Daviaud , Marcin Jurdziński , K. S. Thejaswini

An improved translation from alternating parity automata on infinite words to alternating weak automata is given. The blow-up of the number of states is related to the size of the smallest universal ordered trees and hence it is…

Formal Languages and Automata Theory · Computer Science 2020-01-15 Laure Daviaud , Marcin Jurdziński , Karoliina Lehtinen

We consider two-player games played in real time on game structures with clocks and parity objectives. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the…

Logic in Computer Science · Computer Science 2008-07-09 Krishnendu Chatterjee , Thomas A. Henzinger , Vinayak Prabhu

Parys has recently proposed a quasi-polynomial version of Zielonka's recursive algorithm for solving parity games. In this brief note we suggest a variation of his algorithm that improves the complexity to meet the state-of-the-art…

Computer Science and Game Theory · Computer Science 2019-06-06 Karoliina Lehtinen , Sven Schewe , Dominik Wojtczak

We give an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, for the case where the players are restricted to finite-memory strategies. First, we describe a general framework, where…

Computer Science and Game Theory · Computer Science 2013-06-14 Parosh Aziz Abdulla , Lorenzo Clemente , Richard Mayr , Sven Sandberg

Parity games are games that are played on directed graphs whose vertices are labeled by natural numbers, called priorities. The players push a token along the edges of the digraph. The winner is determined by the parity of the greatest…

Computer Science and Game Theory · Computer Science 2015-03-20 Christoph Dittmann , Stephan Kreutzer , Alexandru I. Tomescu

Mean-payoff games on timed automata are played on the infinite weighted graph of configurations of priced timed automata between two players, Player Min and Player Max, by moving a token along the states of the graph to form an infinite…

Computer Science and Game Theory · Computer Science 2020-01-16 Shibashis Guha , Marcin Jurdzinski , Krishna S. , Ashutosh Trivedi

We consider turn-based stochastic two-player games with a combination of a parity condition that must hold surely, that is in all possible outcomes, and of a parity condition that must hold almost-surely, that is with probability 1. The…

Computer Science and Game Theory · Computer Science 2026-01-08 Laurent Doyen , Shibashis Guha

Classical objectives in two-player zero-sum games played on graphs often deal with limit behaviors of infinite plays: e.g., mean-payoff and total-payoff in the quantitative setting, or parity in the qualitative one (a canonical way to…

Logic in Computer Science · Computer Science 2016-09-21 Véronique Bruyère , Quentin Hautem , Mickael Randour

The parity index problem of tree automata asks, given a regular tree language $L$ and a set of priorities $J$, is $L$ $J$-feasible, that is, recognised by a nondeterministic parity automaton with priorities $J$? This is a long-standing open…

Formal Languages and Automata Theory · Computer Science 2025-04-30 Olivier Idir , Karoliina Lehtinen

The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…

Computer Science and Game Theory · Computer Science 2020-01-16 John Fearnley , Marcin Jurdziński , Rahul Savani