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Benchmarks for Parity Games
[chapter]
2015
Lecture Notes in Computer Science
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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
2018
Electronic Proceedings in Theoretical Computer Science
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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]
2015
arXiv
pre-print
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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
2005
International Journal on Software Tools for Technology Transfer (STTT)
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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
2003
Electronical Notes in Theoretical Computer Science
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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]
2017
Lecture Notes in Computer Science
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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
2020
International Conference on Concurrency Theory
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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]
2002
Lecture Notes in Computer Science
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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]
2020
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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
2001
Information and Computation
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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]
1996
Lecture Notes in Computer Science
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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
1996
BRICS Report Series
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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]
2021
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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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