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