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Parameterized Algorithms for Parity Games [chapter]

Jakub Gajarský, Michael Lampis, Kazuhisa Makino, Valia Mitsou, Sebastian Ordyniak
2015 Lecture Notes in Computer Science  
We complement these results with some algorithmic lower bounds which, among others, rule out a possible avenue for improving the bestknown sub-exponential time algorithm for parity games.  ...  In this paper we adopt a parameterized approach which is more inspired by well-known (non-parameterized) algorithms for this problem.  ...  Acknowledgements We would like to thank Danupon Nanongkai for suggesting this problem and for our useful discussions.  ... 
doi:10.1007/978-3-662-48054-0_28 fatcat:nh6whrx2jvdxti4x37wv4ks4ye

Parameterized complexity of games with monotonically ordered omega-regular objectives

Véronique Bruyère, Quentin Hautem, Jean-François Raskin, Michael Wagner
2018 International Conference on Concurrency Theory  
objectives, ordered objectives, parameterized complexity  ...  We also provide polynomial time algorithms for Büchi, coBüchi and explicit Muller objectives for a large subclass of monotonic preorders that includes among others the lexicographic preorder.  ...  . , Ω n , ) be the lexicographic parity game where Ω i = Parity(p i ) for all i.  ... 
doi:10.4230/lipics.concur.2018.29 dblp:conf/concur/BruyereHR18 fatcat:4soidjklsjho3gkesl2bwtwahi

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

Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL

Martin Zimmermann
2015 Electronic Proceedings in Theoretical Computer Science  
time algorithm for solving games.  ...  We continue the investigation of parameterized extensions of Linear Temporal Logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential  ...  model checking, and a doubly-exponential time algorithm for solving games.  ... 
doi:10.4204/eptcs.193.11 fatcat:nkemqrgnljbixf7iun3vpqwkge

Parameterized linear temporal logics meet costs: still not costlier than LTL

Martin Zimmermann
2016 Acta Informatica  
time algorithm for solving games.  ...  We continue the investigation of parameterized extensions of Linear Temporal Logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential  ...  model checking, and a doubly-exponential time algorithm for solving games.  ... 
doi:10.1007/s00236-016-0279-9 fatcat:zipkg4kqqnh6vdpxs32nodqrka

Parameterized complexity of games with monotonically ordered ω-regular objectives [article]

Véronique Bruyère, Quentin Hautem, Jean-François Raskin
2018 arXiv   pre-print
We also provide polynomial time algorithms for Büchi, coBüchi and explicit Muller objectives for a large subclass of monotonic preorders that includes among others the lexicographic preorder.  ...  In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems.  ...  We would like to thank Antonia Lechner for useful discussions.  ... 
arXiv:1707.05968v4 fatcat:x6czu4jnr5hnda2bmf6sjjo3nq

Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL (full version) [article]

Martin Zimmermann
2016 arXiv   pre-print
time algorithm for solving games.  ...  We continue the investigation of parameterized extensions of Linear Temporal Logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential  ...  model checking, and a doubly-exponential time algorithm for solving games.  ... 
arXiv:1505.06953v5 fatcat:4upvppw5qfhxvpl7uan73ma22m

The 4th Reactive Synthesis Competition (SYNTCOMP 2017): Benchmarks, Participants & Results

Swen Jacobs, Nicolas Basset, Roderick Bloem, Romain Brenguier, Maximilien Colange, Peter Faymonville, Bernd Finkbeiner, Ayrat Khalimov, Felix Klein, Thibaud Michaud, Guillermo A. Pérez, Jean-François Raskin (+2 others)
2017 Electronic Proceedings in Theoretical Computer Science  
of SYNTCOMP 2016 was supported by the Austrian Science Fund (FWF) through project RiSE (S11406-N23) and by the German Research Foundation (DFG) through project "Automatic Synthesis of Distributed and Parameterized  ...  that solve such parity games: the well-known recursive algorithm by Zielonka [44] , and the recent quasi-polynomial time algorithm by Calude et al  ...  Here, the controller wins the parity game (recall that such games are determined [34] ) if and only if the original instance of the reactive synthesis problem has a solution. ltlsynt implements two algorithms  ... 
doi:10.4204/eptcs.260.10 fatcat:k66mstfsmzgmbor32elcwfuvgi

Decomposition theorems and model-checking for the modalμ-calculus

Mikolaj Bojanczyk, Christoph Dittmann, Stephan Kreutzer
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
We prove a general decomposition theorem for the modal μ-calculus L_μ in the spirit of Feferman and Vaught's theorem for disjoint unions.  ...  As far as we are aware, these are the first fpt results for L_μ which do not follow from embedding into monadic second-order logic.  ...  Hence, by translating into parity games we would not obtain fpt algorithms.  ... 
doi:10.1145/2603088.2603144 dblp:conf/csl/BojanczykDK14 fatcat:vfhrvywtezbvjis7i3mglnqzfq

Parameterized Games and Parameterized Automata

Arno Pauly
2018 Electronic Proceedings in Theoretical Computer Science  
We introduce a way to parameterize automata and games on finite graphs with natural numbers.  ...  The main technical result is that in games, a player can win for some values of the parameters at all, if she can win for some values below an exponential bound.  ...  Acknowledgements I am grateful to Ismaël Jecker and Marie Van den Bogaard for discussion leading to the inception of this work.  ... 
doi:10.4204/eptcs.277.3 fatcat:r3m5xlpdrnblxbgujfd3tfmuga

Digraph width measures in parameterized algorithmics

Robert Ganian, Petr Hliněný, Joachim Kneis, Alexander Langer, Jan Obdržálek, Peter Rossmanith
2014 Discrete Applied Mathematics  
In contrast to undirected width measures (such as treewidth or clique-width), which have provided many important algorithmic applications, analogous measures for digraphs such as DAGwidth or Kelly-width  ...  Several recent papers, e.g. those of Kreutzer-Ordyniak, Dankelmann-Gutin-Kim, or Lampis-Kaouri-Mitsou, have given some evidence for this.  ...  Games (Parity) and LTL-model checking (φ-LTLmc).  ... 
doi:10.1016/j.dam.2013.10.038 fatcat:jw3g26o5gvc7dnk4mhsp2nnmkm

The Reactive Synthesis Competition (SYNTCOMP): 2018-2021 [article]

Swen Jacobs, Guillermo A. Perez, Remco Abraham, Veronique Bruyere, Michael Cadilhac, Maximilien Colange, Charly Delfosse, Tom van Dijk, Alexandre Duret-Lutz, Peter Faymonville, Bernd Finkbeiner, Ayrat Khalimov (+13 others)
2022 arXiv   pre-print
The game is then solved using a combination of the recursive algorithm for generalized parity games (Chatterjee et al, 2007) and incomplete polynomial-time algorithms, called partial solvers, presented  ...  For parity games derived from practical examples, the purely symbolic approach performs very well; for contrived artificial constructions, solving an explicit parity game in Oink is superior, though the  ... 
arXiv:2206.00251v1 fatcat:qvg2cqgvjvaa7kpfd3nrbj4ahu

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

Controlling a Population [article]

Nathalie Bertrand, Hugo Gimbert
2017 arXiv   pre-print
This gives rise to a parameterized control problem (where control refers to 2 player games), namely the population control problem: can Controller control the m-population game for all m ∈ N whatever Agents  ...  The first player (Controller) chooses actions, and the second player (Agents) resolves non-determinism for each agent. The game with m agents is called the m-population game.  ...  Acknowledgement: We are grateful to Gregory Batt for fruitful discussions concerning the biological setting. Thanks to Mahsa Shirmohammadi for interesting discussions.  ... 
arXiv:1707.02058v1 fatcat:m3hv6474sbcg3ovgm5xbdrnc7m

Energy Parity Games [chapter]

Krishnendu Chatterjee, Laurent Doyen
2010 Lecture Notes in Computer Science  
As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.  ...  be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games.  ...  Henzinger and Barbara Jobstmann for inspiring discussions, and Patricia Bouyer, Nicolas Markey, Jörg Olschewski, and Michael Ummels for helpful comments on a preliminary draft.  ... 
doi:10.1007/978-3-642-14162-1_50 fatcat:d6sj3bzgqveiteh67hsacgmswm
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