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Fatal Attractors in Parity Games [chapter]

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2013 Lecture Notes in Computer Science  
We study a new form of attractor in parity games and use it to define solvers that run in PTIME and are partial in that they do not solve all games completely.  ...  For one partial solver we prove that its runtime is in O(| V | 3 ), that its output game is independent of the order in which attractors are computed, and that it solves all Büchi games.  ...  work well on many games, whether partial solvers can be components of more efficient complete solvers, and whether there are interesting subclasses of parity games for which partial solvers completely  ... 
doi:10.1007/978-3-642-37075-5_3 fatcat:uxqp357lvjb7pi5jv7e552hg24

Partial Solvers for Parity Games: Effective Polynomial-Time Composition

Patrick Ah-Fat, Michael Huth
2016 Electronic Proceedings in Theoretical Computer Science  
Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes.  ...  For one of these polynomial-time partial solvers not even a sole random game from a few billion random games of varying configuration was found that it won't solve completely.  ...  Acknowledgements: We thank Nir Piterman very much for his comments on this work.  ... 
doi:10.4204/eptcs.226.1 fatcat:f73scd3kwrcrrahdfi4fknb46y

Fatal Attractors in Parity Games: Building Blocks for Partial Solvers [article]

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2014 arXiv   pre-print
For one partial solver we prove that its run-time is at most cubic in the number of nodes in the parity game, that its output game is independent of the order in which monotone attractors are computed,  ...  Attractors in parity games are a technical device for solving "alternating" reachability of given node sets.  ...  We want to design and evaluate a new form of "partial" parity game solver.  ... 
arXiv:1405.0386v2 fatcat:2psoi2zpirdghedq67ip4hooc4

Static Analysis of Parity Games: Alternating Reachability Under Parity [chapter]

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2015 Lecture Notes in Computer Science  
We here mean to provide such robust foundations for deeper analysis through a new form of game, alternating reachability under parity.  ...  A recent approach to studying this problem has been the design of partial solvers, algorithms that run in polynomial time and that may only solve parts of a parity game.  ...  In [14] , a transformation is studied that can map a partial solver ρ for parity games to another partial solver lift(ρ) that first applies ρ until it has no effect on the residual game.  ... 
doi:10.1007/978-3-319-27810-0_8 fatcat:co2qjkdsunhnrjzc32bklgutcy

On-The-Fly Solving for Symbolic Parity Games [article]

Maurice Laveaux, Wieger Wesselink, Tim A.C. Willemse
2022 arXiv   pre-print
Furthermore, we define partial solving techniques for incomplete parity games and show how these can be made resilient to work directly on the incomplete game, rather than on a set of safe vertices.  ...  For many of these decision problems we are only interested in the solution for a designated vertex in the game.  ...  Acknowledgements We would like to thank Jeroen Meijer and Tom van Dijk for their help regarding the Sylvan library when implementing our prototype.  ... 
arXiv:2201.09607v1 fatcat:zulfhot6efeypnv6pnsvd7drje

Solving Parity Games in Practice [chapter]

Oliver Friedmann, Martin Lange
2009 Lecture Notes in Computer Science  
The main contribution is a suggestion on how to solve parity games efficiently in practice: we present a generic solver that intertwines optimisations with any of the existing parity game algorithms which  ...  Parity games are 2-player games of perfect information and infinite duration that have important applications in automata theory and decision procedures (validity as well as model checking) for temporal  ...  An efficient parity game solver may be extendable to efficient solvers for those games as well.  ... 
doi:10.1007/978-3-642-04761-9_15 fatcat:lbvjz7tbwzgjvhae3ykkala2ei

Strix: Explicit Reactive Synthesis Strikes Back! [chapter]

Philipp J. Meyer, Salomon Sickert, Michael Luttenberger
2018 Lecture Notes in Computer Science  
Strix is a new tool for reactive LTL synthesis combining a direct translation of LTL formulas into deterministic parity automata (DPA) and an efficient, multi-threaded explicit state solver for parity  ...  In brief, Strix (1) decomposes the given formula into simpler formulas, (2) translates these on-the-fly into DPAs based on the queries of the parity game solver, (3) composes the DPAs into a parity game  ...  The parity game solver runs in parallel to the arena construction on the partially constructed game in order to guide the translation process, with the possibility for early termination when a winning  ... 
doi:10.1007/978-3-319-96145-3_31 fatcat:f3gcoh23ujd3vadfvpmj3tqpga

A Comparison of BDD-Based Parity Game Solvers

Lisette Sanchez, Wieger Wesselink, Tim A.C. Willemse
2018 Electronic Proceedings in Theoretical Computer Science  
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.  ...  In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz.  ...  out-degree random games generated using randomgame N N 1 2 x; • dense random games generated using randomgame N N 1 N x; For each class of random games and each value of N we generated 20 parity games  ... 
doi:10.4204/eptcs.277.8 fatcat:76qxzmcteffbrpxvapewuqgwty

A workbench for preprocessor design and evaluation: toward benchmarks for parity games

Michael Huth, Nir Piterman, Huaxin Wang
2009 Electronic Communications of the EASST  
This workbench is aimed at facilitating two activities: to aid in the design, validation, and evaluation of preprocessors for parity game solvers; and to aid in the generation of benchmark parity games  ...  We describe a prototype workbench for the study of parity games and their solvers.  ...  Acknowledgements: This research was, in part, supported by the UK EPSRC project "Complete and Efficient Checks for Branching-Time Abstractions"(EP/E028985/1). Bibliography  ... 
doi:10.14279/tuj.eceasst.23.324 dblp:journals/eceasst/HuthPW09 fatcat:y5u3kqehkvgxxdhwwrjrkuonyi

Solving parity games via priority promotion

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2018 Formal methods in system design  
To the first family belongs the divide et impera solution originally proposed by McNaughton [39] for Muller games and adapted to parity games by Zielonka [54] .  ...  The main contribution of the paper is a new algorithm for solving parity games, based on the notions of quasi dominion and priority promotion.  ...  and 10 random games were generated for each pair of n and k.  ... 
doi:10.1007/s10703-018-0315-1 fatcat:qb4e5r2lr5fozgtn5p4liiaqy4

Solving Parity Games via Priority Promotion [chapter]

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2016 Lecture Notes in Computer Science  
We consider parity games, a special form of two-player infinite-duration games on numerically labelled graphs, whose winning condition requires that the maximal value of a label occurring infinitely often  ...  Parity games also have great practical interest, as they arise in many fields of theoretical computer science, most notably logic, automata theory, and formal verification.  ...  , and 10 random games were generated for each pair of n and k.  ... 
doi:10.1007/978-3-319-41540-6_15 fatcat:4wj7uh75wberbfnlzdn6ozypme

TWO LOCAL STRATEGY ITERATION SCHEMES FOR PARITY GAME SOLVING

OLIVER FRIEDMANN, MARTIN LANGE
2012 International Journal of Foundations of Computer Science  
Some of the best algorithms for solving parity game are strategy iteration algorithms. These are global in nature since they require the entire parity game to be present at the beginning.  ...  We also compare them empirically with existing global strategy iteration algorithms and the currently only other local algorithm for solving parity games.  ...  We would like to thank the anonymous referees for their thorough reports containing many comments that helped to improve the presentation of this paper.  ... 
doi:10.1142/s0129054112400333 fatcat:phxypuyg2za6tbo5sv4xc3wcle

Oink: An Implementation and Evaluation of Modern Parity Game Solvers [chapter]

Tom van Dijk
2018 Lecture Notes in Computer Science  
We further present a comprehensive empirical evaluation of modern parity game algorithms and solvers, both on real world benchmarks and randomly generated games.  ...  We implement a new and easy to extend tool Oink, which is a high-performance implementation of modern parity game algorithms.  ...  We thank Tim Willemse and John Fearnley for their helpful comments and Jaco van de Pol for the use of their computer cluster.  ... 
doi:10.1007/978-3-319-89960-2_16 fatcat:r3nmggdbsjhlnggq5qc5r2x5de

The Rabin index of parity games: Its complexity and approximation

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2015 Information and Computation  
We evaluate this efficient algorithm as a preprocessor of solvers in detailed experiments: for Zielonka's solver on random and structured parity games and for our partial solver psolB on random games.  ...  We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure.  ...  Acknowledgments We thank the anonymous referees for their careful and critical review of the submitted manuscript.  ... 
doi:10.1016/j.ic.2015.06.005 fatcat:i6tf7qwmxnfthozwzafs7uotve

Solving parity games by a reduction to SAT

Keijo Heljanko, Misa Keinänen, Martin Lange, Ilkka Niemelä
2012 Journal of computer and system sciences (Print)  
This paper presents a reduction from the problem of solving parity games to the satisfiability problem in propositional logic (SAT).  ...  The reduction is motivated by the success of SAT solvers in symbolic verification, bounded model checking in particular.  ...  successful discussions about solving parity games of bounded tree-and clique-width, and Marcin Jurdziński for inspiring comments about difficult parity games.  ... 
doi:10.1016/j.jcss.2011.05.004 fatcat:lwolqad7gnhe5b6yl3wsnz4dzi
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