English
Related papers

Related papers: Simple Fixpoint Iteration To Solve Parity Games

200 papers

The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…

Logic in Computer Science · Computer Science 2026-01-23 Paolo Baldan , Sebastian Gurke , Barbara König , Florian Wittbold

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…

Logic in Computer Science · Computer Science 2017-09-05 Helle Hvid Hansen , Clemens Kupke , Johannes Marti , Yde Venema

Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently…

Logic in Computer Science · Computer Science 2018-09-11 Lisette Sanchez , Wieger Wesselink , Tim A. C. Willemse

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…

Logic in Computer Science · Computer Science 2018-01-30 John Fearnley , Sanjay Jain , Sven Schewe , Frank Stephan , Dominik Wojtczak

We present a new tool for verification of modal mu-calculus formulae for process specifications, based on symbolic parity games. It enhances an existing method, that first encodes the problem to a Parameterised Boolean Equation System…

Logic in Computer Science · Computer Science 2014-07-31 Gijs Kant , Jaco van de Pol

We study the process theoretic notion of stuttering equivalence in the setting of parity games. We demonstrate that stuttering equivalent vertices have the same winner in the parity game. This means that solving a parity game can be…

Logic in Computer Science · Computer Science 2025-08-08 Sjoerd Cranen , Jeroen J. A. Keiren , Tim A. C. Willemse

We show a new simple algorithm that solves the model-checking problem for recursion schemes: check whether the tree generated by a given higher-order recursion scheme is accepted by a given alternating parity automaton. The algorithm…

Logic in Computer Science · Computer Science 2021-05-06 Paweł Parys

Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has…

Numerical Analysis · Mathematics 2020-06-29 Diego Zabaljauregui

Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…

Logic in Computer Science · Computer Science 2023-11-08 Philippe Heim , Rayna Dimitrova

An attractor decomposition meta-algorithm for solving parity games is given that generalises the classic McNaughton-Zielonka algorithm and its recent quasi-polynomial variants due to Parys (2019), and to Lehtinen, Schewe, and Wojtczak…

Data Structures and Algorithms · Computer Science 2022-08-30 Marcin Jurdziński , Rémi Morvan , K. S. Thejaswini

We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the…

Logic in Computer Science · Computer Science 2015-07-01 Diana Fischer , Lukasz Kaiser

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

Fixpoints are ubiquitous in computer science and when dealing with quantitative semantics and verification one often considers least fixpoints of (higher-dimensional) functions over the non-negative reals. We show how to approximate the…

Logic in Computer Science · Computer Science 2025-06-16 Paolo Baldan , Sebastian Gurke , Barbara König , Tommaso Padoan , Florian Wittbold

We study the underlying mathematical properties of various partial order models of concurrency based on transition systems, Petri nets, and event structures, and show that the concurrent behaviour of these systems can be captured in a…

Logic in Computer Science · Computer Science 2010-11-05 Julian Gutierrez

We introduce the countdown $\mu$-calculus, an extension of the modal $\mu$-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties…

Logic in Computer Science · Computer Science 2022-08-02 Jędrzej Kołodziejski , Bartek Klin

Higher-order modal fixpoint logic (HFL) is a higher-order extension of the modal mu-calculus, and strictly more expressive than the modal mu-calculus. It has recently been shown that various program verification problems can naturally be…

Logic in Computer Science · Computer Science 2019-08-29 Youkichi Hosoi , Naoki Kobayashi , Takeshi Tsukada

Calude, Jain, Khoussainov, Li, and Stephan (2017) proposed a quasi-polynomial-time algorithm solving parity games. After this breakthrough result, a few other quasi-polynomial-time algorithms were introduced; none of them is easy to…

Formal Languages and Automata Theory · Computer Science 2019-04-30 Paweł Parys

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

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…

Data Structures and Algorithms · Computer Science 2026-03-11 Daniele Dell'Erba , Arthur Dumas , Sven Schewe

Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms.…

Logic in Computer Science · Computer Science 2013-07-18 Maciej Gazda , Tim A. C. Willemse