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Benchmarks for Parity Games [chapter]

Jeroen J. A. Keiren
2015 Lecture Notes in Computer Science  
With this work we provide a starting point for further experimentation with parity games.  ...  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 Comparison of BDD-Based Parity Game Solvers

Lisette Sanchez, Wieger Wesselink, Tim A.C. Willemse
2018 Electronic Proceedings in Theoretical Computer Science  
In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz.  ...  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 essentially based on the reduction of the parity game solving problem to the modal µ-calculus model checking problem.  ... 
doi:10.4204/eptcs.277.8 fatcat:76qxzmcteffbrpxvapewuqgwty

Benchmarks for Parity Games (extended version) [article]

Jeroen J.A. Keiren
2015 arXiv   pre-print
With this work we provide a starting point for further experimentation with parity games.  ...  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.  ... 
arXiv:1407.3121v2 fatcat:lefwv7otkfcjblw3e2abwlesb4

Symbolic computational techniques for solving games

Rajeev Alur, P. Madhusudan, Wonhong Nam
2005 International Journal on Software Tools for Technology Transfer (STTT)  
We also show how some of these techniques can be adopted to solve safety games.  ...  For reachability games, the first technique employs symbolic fixed-point computation using ordered binary decision diagrams (BDDs) [9] .  ...  While µ-calculus model checking can be seen to be equivalent to evaluating infinite parity games on finite graphs, the µ-calculus also trivially encodes solutions to reachability games.  ... 
doi:10.1007/s10009-004-0179-0 fatcat:dfovppghm5e5vdahquqdz6ml2i

Symbolic Computational Techniques for Solving Games

P. Madhusudan, Wonhong Nam, Rajeev Alur
2003 Electronical Notes in Theoretical Computer Science  
We also show how some of these techniques can be adopted to solve safety games.  ...  For reachability games, the first technique employs symbolic fixed-point computation using ordered binary decision diagrams (BDDs) [9] .  ...  While µ-calculus model checking can be seen to be equivalent to evaluating infinite parity games on finite graphs, the µ-calculus also trivially encodes solutions to reachability games.  ... 
doi:10.1016/s1571-0661(05)82544-7 fatcat:z5bww4gxrnatxgyjylynggw3ze

Parity Games on Bounded Phase Multi-pushdown Systems [chapter]

Mohamed Faouzi Atig, Ahmed Bouajjani, K. Narayan Kumar, Prakash Saivasan
2017 Lecture Notes in Computer Science  
In this paper we address the problem of solving parity games over the configuration graphs of bounded phase multi-pushdown systems.  ...  A non-elementary decision procedure was proposed for this problem by A. Seth. In this paper, we provide a simple and inductive construction to solve this problem.  ...  The proof of the theorem is obtained by inductively solving the k bounded-phase parity game.  ... 
doi:10.1007/978-3-319-59647-1_21 fatcat:gyox52gcgng3nmi4f7gvhnlxqa

Abstraction, Up-To Techniques and Games for Systems of Fixpoint Equations

Paolo Baldan, Barbara König, Tommaso Padoan, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
Additionally, relying on the approximation theory, we can characterise the solution of systems of fixpoint equations over complete lattices in terms of a suitable parity game, generalising some recent  ...  The game view opens the way for the development of local algorithms for characterising the solution of such equation systems and we explore some special cases.  ...  Evaluating µ-calculus formulae on a transition system can be reduced to solving a parity game and the exact complexity of this task is still open.  ... 
doi:10.4230/lipics.concur.2020.25 dblp:conf/concur/Baldan0P20 fatcat:ntk5jqiye5buxfc6gs22phblny

Algorithms for Parity Games [chapter]

Hartmut Klauck
2002 Lecture Notes in Computer Science  
Parity games are equivalent via linear time reductions to the problem of modal µ-calculus model checking (see Chapters 10 and 9), and this model checking problem plays a major role in computer-aided verification  ...  Recall that in a parity game we are given a (finite) graph with vertices labeled by natural numbers.  ...  The modal µ-calculus was defined first by Kozen in [100], see Chapter 10.  ... 
doi:10.1007/3-540-36387-4_7 fatcat:2xu24otqbzarfpfetg5574blza

Size matters in the modal μ-calculus [article]

Clemens Kupke and Johannes Marti and Yde Venema
2020 arXiv   pre-print
Building on work by Bruse, Friedmann Lange, we compare two size measures for μ-calculus formulas: subformula-size,i.e. , the number of subformulas of the given formula, and closure-size.  ...  We define subformula-size and closure-size and recall that a μ-calculus formula can be transformed into a parity formula of size linear wrt subformula size, and give a construction that transforms a μ-calculus  ...  between µML model checking and the problem of solving parity games.  ... 
arXiv:2010.14430v1 fatcat:fvndfh2gkvcm3fe7dfbtk6wo34

Leveraging the Power of Graph Algorithms: Efficient Algorithms for Computer-Aided Verification [article]

Alexander Svozil
2022 arXiv   pre-print
The first quasi-polynomial time symbolic algorithm for parity objectives in game graphs.  ...  We break a long-standing running time bound for MEC decomposition from the '90s by providing a sub-quadratic time symbolic algorithm.  ...  Moreover, [173] presents a µ-calculus formula describing the winning regions of the parity game with alternation depth based on the register-index.  ... 
arXiv:2202.02660v1 fatcat:pjrm5gx5mbgsxefhowxgryccmy

Pushdown Processes: Games and Model-Checking

Igor Walukiewicz
2001 Information and Computation  
Games given by transition graphs of pushdown processes are considered.  ...  This fact turns out to be connected with the model checking problem for the pushdown automata and the propositional µ-calculus. It is show that this model checking problem is DEXPTIME-complete.  ...  µ-calculus to the model checking problem for finite transition systems and the µ-calculus.  ... 
doi:10.1006/inco.2000.2894 fatcat:im5voxueufg2zkejb5fpznz2k4

Pushdown processes: Games and model checking [chapter]

Igor Walukiewicz
1996 Lecture Notes in Computer Science  
Games given by transition graphs of pushdown processes are considered.  ...  This fact turns out to be connected with the model checking problem for the pushdown automata and the propositional µ-calculus. It is show that this model checking problem is DEXPTIME-complete.  ...  µ-calculus to the model checking problem for finite transition systems and the µ-calculus.  ... 
doi:10.1007/3-540-61474-5_58 fatcat:ldyhqmytc5hevdsfvdiksymopa

Pushdown Processes: Games and Model Checking

Igor Walukiewicz
1996 BRICS Report Series  
Games given by transition graphs of pushdown processes are considered.  ...  <br />It is shown that if there is a winning strategy in such a<br />game then there is a winning strategy that is realized by a pushdown<br />process.  ...  µ-calculus to the model checking problem for finite transition systems and the µ-calculus.  ... 
doi:10.7146/brics.v3i54.20057 fatcat:pzvwnk4otbbuvcu2s2olplfizq

Fixpoint Games on Continuous Lattices [article]

Paolo Baldan, Barbara König, Tommaso Padoan, Christina Mika-Michalski
2021 arXiv   pre-print
For powerset lattices the fixpoint game is intimately connected with classical parity games for μ-calculus model-checking, whose solution can exploit as a key tool Jurdziński's small progress measures.  ...  We refine this characterisation by introducing the notion of selection that allows one to constrain the plays in the parity game, enabling an effective (and possibly efficient) solution of the game, and  ...  Furthermore we are grateful to Clemens Kupke for bringing fixpoint games to our attention.  ... 
arXiv:1810.11404v2 fatcat:eazlulkcdfhzte44tldfzghei4

Featured Games [article]

Uli Fahrenberg, Axel Legay
2020 arXiv   pre-print
A prominent example is mu-calculus model checking, which is generally done by translating to parity games, but also many quantitative model-checking problems can be reduced to (quantitative) games.  ...  .\ introduce parity games with variability in order to develop family-based mu-calculus model checking of featured transition systems.  ...  A prominent example is µ-calculus model checking, which is generally done by translating to parity games [5] , but also many quantitative model-checking problems can be reduced to (quantitative) games  ... 
arXiv:2005.05666v2 fatcat:o2tzdwymk5faloap5nqvhlzvia
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