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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.  ...  game based on LTSmin (pbes2lts-sym), and a new symbolic parity game solver tool (spgsolver).  ... 
doi:10.4204/eptcs.159.2 fatcat:oyzkxkthrjdfpdr7yhxlcjkevy

Generalized Parity Games [chapter]

Krishnendu Chatterjee, Thomas A. Henzinger, Nir Piterman
Foundations of Software Science and Computational Structures  
We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them generalized parity games.  ...  The resulting complexity of solving generalized parity games is n O( √ n) · (k·d)! d! k .  ...  when these games are solved as Rabin or Streett games). We generalize the techniques of the subexponential algorithm for solving parity games [11] to generalized parity games.  ... 
doi:10.1007/978-3-540-71389-0_12 dblp:conf/fossacs/ChatterjeeHP07 fatcat:r4jeslfyz5bcpedafmyk4qormy

Benchmarks for Parity Games [chapter]

Jeroen J. A. Keiren
2015 Lecture Notes in Computer Science  
We give an overview of the parity games, including a description of how they have been generated.  ...  With this work we provide a starting point for further experimentation with parity games.  ...  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

Benchmarks for Parity Games (extended version) [article]

Jeroen J.A. Keiren
2015 arXiv   pre-print
We give an overview of the parity games, including a description of how they have been generated.  ...  With this work we provide a starting point for further experimentation with parity games.  ...  Acknowledgements For generating the parity games described in the paper, a large number of tools have been used.  ... 
arXiv:1407.3121v2 fatcat:lefwv7otkfcjblw3e2abwlesb4

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  ...  In this paper we investigate practical aspects of solving parity games.  ...  A Generic Solver We propose to solve parity games using the following generic algorithm which takes as parameter a real solver and applies it only where necessary.  ... 
doi:10.1007/978-3-642-04761-9_15 fatcat:lbvjz7tbwzgjvhae3ykkala2ei

Time and Parallelizability Results for Parity Games with Bounded Treewidth [chapter]

John Fearnley, Sven Schewe
2012 Lecture Notes in Computer Science  
This is in stark contrast to the general parity game problem, which is known to be P-hard, and thus unlikely to be contained in NC.  ...  , and number of priorities in the parity game.  ...  in the parity game, and k is the treewidth of the game.  ... 
doi:10.1007/978-3-642-31585-5_20 fatcat:s222lmrcubb3fhgexdch7nv57a

Parity Games with Weights

Sven Schewe, Alexander Weinert, Martin Zimmermann, Michael Wagner
2018 Annual Conference for Computer Science Logic  
These extensions include parity games with energy and payoff conditions as well as finitary parity games and their generalization to parity games with costs.  ...  Quantitative extensions of parity games have recently attracted significant interest.  ...  This property calls for a generalization to different cost models, and a first generalization has been made with the introduction of parity games with costs [14] .  ... 
doi:10.4230/lipics.csl.2018.36 dblp:conf/csl/ScheweW018 fatcat:edv54p2pubdstkxbgtr4vpnh6e

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

Michael Huth, Jim Huan-Pu Kuo, Nir Piterman
2015 Lecture Notes in Computer Science  
nodes in its greatest fixed point are won by said player in the parity game.  ...  It is well understood that solving parity games is equivalent, up to polynomial time, to model checking of the modal mu-calculus.  ...  This is why we focused our experimental effort here an random parity games. We now report our experiments we did on randomly generated games.  ... 
doi:10.1007/978-3-319-27810-0_8 fatcat:co2qjkdsunhnrjzc32bklgutcy

Safety first: A two-stage algorithm for LTL games

Saqib Sohail, Fabio Somenzi
2009 2009 Formal Methods in Computer-Aided Design  
An implementation can be obtained from a winning strategy derived from a suitable generalized parity game in which each property produces a parity acceptance condition.  ...  We show how this can be exploited to play the game in two stages and substantially speed up synthesis without sacrificing generality and conciseness of specification. 978-1-4244-4966-8/09/$25.00 ©2009  ...  Büchi, parity, and disjunctive generalized parity games admit memoryless strategies. The others-generalized Büchi, and conjunctive generalized parity games-admit finite memory strategies [20] .  ... 
doi:10.1109/fmcad.2009.5351138 dblp:conf/fmcad/SohailS09 fatcat:ygq3phzqv5ahpkzfvwzbxhu67m

Cost-Parity and Cost-Streett Games

Nathanael Fijalkow, Martin Zimmermann, Marc Herbstritt
2012 Foundations of Software Technology and Theoretical Computer Science  
For cost-parity games we show that the first player has positional winning strategies and that determining the winner lies in NP ∩ coNP.  ...  We consider two-player games played on graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their  ...  Hence, cost-parity games generalize both parity and finitary parity games. CostParity(Ω) = {ρ ∈ V ω | lim sup k→∞ cor(ρ, k) < ∞} .  ... 
doi:10.4230/lipics.fsttcs.2012.124 dblp:conf/fsttcs/FijalkowZ12 fatcat:4nnmkdmxhzdo7cpwfsralntzey

An Optimal Value Iteration Algorithm for Parity Games [article]

Nathanaël Fijalkow
2018 arXiv   pre-print
The quest for a polynomial time algorithm for solving parity games gained momentum in 2017 when two different quasipolynomial time algorithms were constructed.  ...  This suggests that the succinct progress measure algorithm of Jurdzi\'nski and Lazi\'c is in this framework optimal, and that the polynomial time algorithm for parity games is hiding someplace else.  ...  ALGORITHM 3: The generic value iteration algorithm. Data: A parity game with n vertices and d priorities.  ... 
arXiv:1801.09618v1 fatcat:sknboutetjakvaskzucyxsh64q

The Descriptive Complexity of Modal μ Model-checking Games

Karoliina Lehtinen
2017 Electronic Proceedings in Theoretical Computer Science  
This paper revisits the well-established relationship between the modal mu calculus and parity games to show that it is even more robust than previously known.  ...  Beyond co-B\"uchi, the descriptive complexity of the model-checking parity games of a formula is shown to be an upper bound on its semantic complexity; whether it is also a lower bound remains an open  ...  Without loss of generality, take T to be finitely branching. Let σ be Even's winning strategy in the parity game T × Φ which only sees one play per branch.  ... 
doi:10.4204/eptcs.256.6 fatcat:4ryiv3g6fjdj7kh3ili7epckxe

A difficulty in particular Shannon-like games

Yōhei Yamasaki
1991 Discrete Applied Mathematics  
., A difficulty in particular Shannon-like games, Discrete Applied Mathematics 30 (1991) 87-90. We have a simple theory of strategy far generalized Shannon switching games (on edges).  ...  We shall see that any strategy theory of a certain type cannot be applied either to Hex of 4' vertices or to a certain f-pair game, though it can be applied to all 2-pair games.  ...  Fraenkel for his valuable information on Hex-like games in complexity theory.  ... 
doi:10.1016/0166-218x(91)90017-q fatcat:4motldzxlfgitokblfbnrkq4ky

Quasipolynomial Computation of Nested Fixpoints [chapter]

Daniel Hausmann, Lutz Schröder
2021 Lecture Notes in Computer Science  
s recent quasipolynomial-time parity game solving algorithm essentially shows how to compute the same fixpoint in only quasipolynomially many iterations by reducing parity games to quasipolynomially sized  ...  Universal graphs have been used to modularize this transformation of parity games to equivalent safety games that are obtained by combining the original game with a universal graph.  ...  It has been shown that these histories can be seen as nodes in universal graphs, in a more general reduction of parity games to safety games in which nodes from the parity game are annotated with nodes  ... 
doi:10.1007/978-3-030-72016-2_3 fatcat:up2kucajgbdj5nkkrrkxwq5sqa

Winning Cores in Parity Games

Steen Vester
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
The algorithm returns under-approximations of the winning regions in parity games.  ...  Whether parity games can be solved by a polynomial-time algorithm is a well-studied problem which has not yet been resolved.  ...  In Figure 2 are experimental results on correctness in randomly generated games.  ... 
doi:10.1145/2933575.2933589 dblp:conf/lics/Vester16 fatcat:r5wy4urbrbcklm22dvcainb5n4
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