An Improved Recursive Algorithm for Parity Games

2014 ◽  
Author(s):  
Yao Liu ◽  
Zhenhua Duan ◽  
Cong Tian
Keyword(s):  
Recursive Algorithm ◽  
Parity Games

scholarly journals Improving parity games in practice

2021 ◽  
Author(s):  
Antonio Di Stasio ◽  
Aniello Murano ◽  
Vincenzo Prignano ◽  
Loredana Sorrentino
Keyword(s):  
Programming Languages ◽  
Data Structures ◽  
Directed Graphs ◽  
Recursive Algorithm ◽  
Empirical Evaluation ◽  
Specific Data ◽  
Running Time ◽  
Parity Games ◽  
Random Games

AbstractParity games are infinite-round two-player games played on directed graphs whose nodes are labeled with priorities. The winner of a play is determined by the smallest priority (even or odd) that is encountered infinitely often along the play. In the last two decades, several algorithms for solving parity games have been proposed and implemented in , a platform written in OCaml. includes the Zielonka’s recursive algorithm (, for short) which is known to be the best performing one over random games. Notably, several attempts have been carried out with the aim of improving the performance of in , but with small advances in practice. In this work, we deeply revisit the implementation of by dealing with the use of specific data structures and programming languages such as Scala, Java, C++, and Go. Our empirical evaluation shows that these choices are successful, gaining up to three orders of magnitude in running time over the classic version of the algorithm implemented in .

scholarly journals Parallel Parity Games: a Multicore Attractor for the Zielonka Recursive Algorithm

2017 ◽  
Vol 108 ◽  
pp. 525-534 ◽  
Author(s):  
Rossella Arcucci ◽  
Umberto Marotta ◽  
Aniello Murano ◽  
Loredana Sorrentino
Keyword(s):  
Recursive Algorithm ◽  
Parity Games

scholarly journals A Recursive Approach to Solving Parity Games in Quasipolynomial Time

2022 ◽  
Vol Volume 18, Issue 1 ◽  
Author(s):  
Karoliina Lehtinen ◽  
Paweł Parys ◽  
Sven Schewe ◽  
Dominik Wojtczak
Keyword(s):  
State Of The Art ◽  
Recursive Algorithm ◽  
The State ◽  
Parity Games ◽  
The Many

Zielonka's classic recursive algorithm for solving parity games is perhaps the simplest among the many existing parity game algorithms. However, its complexity is exponential, while currently the state-of-the-art algorithms have quasipolynomial complexity. Here, we present a modification of Zielonka's classic algorithm that brings its complexity down to $n^{O\left(\log\left(1+\frac{d}{\log n}\right)\right)}$, for parity games of size $n$ with $d$ priorities, in line with previous quasipolynomial-time solutions.

LMI-based hybrid temporal-spatial differential control design for a class of Euler-Bernoulli beam system

2021 ◽  
pp. 095440622110036
Author(s):  
Jiaqi Zhong ◽  
Xiaolei Chen ◽  
Yupeng Yuan ◽  
Jiajia Tan
Keyword(s):  
Vibration Suppression ◽  
Direct Method ◽  
Recursive Algorithm ◽  
Linear Matrix ◽  
Bernoulli Beam ◽  
Hybrid Controller ◽  
Beam System ◽  
Active Vibration ◽  
Differential Control ◽  
Euler Bernoulli Beam

This paper addresses the problem of active vibration suppression for a class of Euler-Bernoulli beam system. The objective of this paper is to design a hybrid temporal-spatial differential controller, which is involved with the in-domain and boundary actuators, such that the closed-loop system is stable. The Lyapunov’s direct method is employed to derive the sufficient condition, which not only can guarantee the stabilization of system, but also can improve the spatial cooperation of actuators. In the framework of the linear matrix inequalities (LMIs) technology, the gain matrices of hybrid controller can obtained by developing a recursive algorithm. Finally, the effectiveness of the proposed methodology is demonstrated by applying a numerical simulation.

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