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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.  ...  In future work, we mean to study the descriptive complexity of the class of output games of a partial solver, for example of psolQ.  ... 
doi:10.1007/978-3-642-37075-5_3 fatcat:uxqp357lvjb7pi5jv7e552hg24

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

Benchmarks for Parity Games [chapter]

Jeroen J. A. Keiren
2015 Lecture Notes in Computer Science  
We propose a benchmark suite for parity games that includes the benchmarks that have been used in the literature, and make it available online.  ...  We give an overview of the parity games, including a description of how they have been generated.  ...  Acknowledgements For generating the parity games described in the paper, a large number of tools have been used.  ... 
doi:10.1007/978-3-319-24644-4_9 fatcat:2ahawarizrhp3lrbaz62nujmhm

A Parity Game Tale of Two Counters [article]

Tom van Dijk
2018 arXiv   pre-print
We present a parameterized parity game called the Two Counters game, which provides an exponential lower bound for a wide range of parity game solving algorithms.  ...  Parity games have important practical applications in formal verification and synthesis, especially for problems related to linear temporal logic and to the modal mu-calculus.  ...  Acknowledgements We thank Veronika Loitzenbauer for the helpful discussions on these and other difficult parity games.  ... 
arXiv:1807.10210v2 fatcat:xvo4cmlk3fgbjj74jqw5ur2th4

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.  ...  However, the algorithm runs on polynomial space, unlike some other known algorithms for solving parity games. Our work relates to research on the descriptive complexity of parity games.  ... 
doi:10.1007/978-3-319-27810-0_8 fatcat:co2qjkdsunhnrjzc32bklgutcy

Attracting Tangles to Solve Parity Games [chapter]

Tom van Dijk
2018 Lecture Notes in Computer Science  
We argue that tangles play a fundamental role in the prominent parity game solving algorithms. We show that tangle learning is competitive in practice and the fastest solver for large random games.  ...  We propose a new algorithm to solve parity games based on learning tangles, which are strongly connected subgraphs for which one player has a strategy to win all cycles in the subgraph.  ...  We thank the anonymous referees for their helpful comments, Jaco van de Pol for the use of the computer cluster, and Armin Biere for generously supporting this research.  ... 
doi:10.1007/978-3-319-96142-2_14 fatcat:4qq7sijjwfck5jxnusrkjiekrm

Solving parity games via priority promotion

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2018 Formal methods in system design  
The main contribution of the paper is a new algorithm for solving parity games, based on the notions of quasi dominion and priority promotion.  ...  In this paper, we propose a new algorithm for the solution of the problem, based on the idea of promoting vertices to higher priorities during the search for winning regions.  ...  On the bright side, the new solution exhibits the best space complexity among the currently known algorithms for parity games.  ... 
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  
In this paper, we propose a new algorithm for the solution of the problem, based on the idea of promoting vertices to higher priorities during the search for winning regions.  ...  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.  ...  On the bright side, the new solution exhibits the best space complexity among the currently known algorithms for parity games.  ... 
doi:10.1007/978-3-319-41540-6_15 fatcat:4wj7uh75wberbfnlzdn6ozypme

The Rabin index of parity games

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2013 Electronic Proceedings in Theoretical Computer Science  
We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure.  ...  Colored game graphs are identified if they determine the same winning regions and strategies, for all ownership structures of nodes.  ...  One approach taken in analyzing the complexity of parity games, and in so hopefully improving the complexity of their solution, is through the study of the descriptive complexity of their underlying game  ... 
doi:10.4204/eptcs.119.6 fatcat:7w7z7mmjkbainfiyf5bo6pwflu

The Rabin Index of Parity Games [chapter]

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2012 Lecture Notes in Computer Science  
We study the descriptive complexity of parity games by taking into account the coloring of their game graphs whilst ignoring their ownership structure.  ...  Colored game graphs are identified if they determine the same winning regions and strategies, for all ownership structures of nodes.  ...  One approach taken in analyzing the complexity of parity games, and in so hopefully improving the complexity of their solution, is through the study of the descriptive complexity of their underlying game  ... 
doi:10.1007/978-3-642-34188-5_25 fatcat:3yluvsk3czbbtec4pyh7nmbwbm

Generating and Solving Symbolic Parity Games

Gijs Kant, Jaco van de Pol
2014 Electronic Proceedings in Theoretical Computer Science  
recursive parity game solving algorithm by Zielonka for symbolic parity games.  ...  We present a new tool for verification of modal mu-calculus formulae for process specifications, based on symbolic parity games.  ...  ), an efficient tool for symbolic instantiation of the PBES to a symbolic parity game based on LTSmin (pbes2lts-sym), and a new symbolic parity game solver tool (spgsolver).  ... 
doi:10.4204/eptcs.159.2 fatcat:oyzkxkthrjdfpdr7yhxlcjkevy

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

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2014 arXiv   pre-print
A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively.  ...  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

A Multi-Core Solver for Parity Games

Jaco van de Pol, Michael Weber
2008 Electronical Notes in Theoretical Computer Science  
We describe a parallel algorithm for solving parity games, with applications in, e.g., modal μ-calculus model checking with arbitrary alternations, and (branching) bisimulation checking.  ...  We evaluate our multicore implementation's behaviour on parity games obtained from μ-calculus model checking problems for a set of communication protocols, randomly generated problem instances, and parametric  ...  Acknowledgement We are indebted to Martin Leucker for pointing us to Jurdzinski's algorithm, and for discussions on the topic during his visit at CWI.  ... 
doi:10.1016/j.entcs.2008.11.011 fatcat:irnvti6zqzbfbmmkyhes376ahu

On Promptness in Parity Games [chapter]

Fabio Mogavero, Aniello Murano, Loredana Sorrentino
2013 Lecture Notes in Computer Science  
In particular, they improve the complexity results of cost and bounded-cost parity games.  ...  Parity games are a powerful formalism for the automatic synthesis and verification of reactive systems.  ...  As games already addressed in literature, we studied cost parity and boundedcost parity and, for both of them, we provided algorithms that improve their known complexity.  ... 
doi:10.1007/978-3-642-45221-5_40 fatcat:4wlbmecubvcypktd23ywqoeklq

A Delayed Promotion Policy for Parity Games

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2016 Electronic Proceedings in Theoretical Computer Science  
Parity games are two-player infinite-duration games on graphs that play a crucial role in various fields of theoretical computer science.  ...  Finding efficient algorithms to solve these games in practice is widely acknowledged as a core problem in formal verification, as it leads to efficient solutions of the model-checking and satisfiability  ...  The literature on the topic is reach of algorithms for solving parity games, which can be mainly classified into two families.  ... 
doi:10.4204/eptcs.226.3 fatcat:6zagd7zjt5fzdfe4ras7yzhy6e
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