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From Quasi-Dominions to Progress Measures
[article]
2021
arXiv
pre-print
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Adding quasi dominions provides additional information on this player that can be leveraged to greatly accelerate convergence to a progress measure. ...
We revisit the approaches to the solution of parity games based on progress measures and show how the notion of quasi dominions can be integrated with those approaches. ...
This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101032464. ...
arXiv:2008.04232v2
fatcat:yerwrduwcbadtfouhpgstc46qu
Solving Mean-Payoff Games via Quasi Dominions
[chapter]
2020
Lecture Notes in Computer Science
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We propose a novel algorithm for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions ...
We show that the integration of the two notions can be highly beneficial and significantly speeds up convergence to the problem solution. ...
On the other hand, the best choice for player in position c is to exit from the weak quasi-dominion Q = {c, d}, by choosing the move (c, a) and lifting its measure from 0 to k. ...
doi:10.1007/978-3-030-45237-7_18
fatcat:2hd5sdmahfbfjbiossv5ivwgbi
A Delayed Promotion Policy for Parity Games
2016
Electronic Proceedings in Theoretical Computer Science
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2016 pre-print arXiv:1609.04087v1 fatcat:pckjo5v4wjbfxkdti5xxvl5daa
Recently, a novel technique to compute dominions, called priority promotion, has been proposed, which is based on the notions of quasi dominion, a relaxed form of dominion, and dominion space. ...
Their solution can be reduced to the problem of identifying sets of positions of the game, called dominions, in each of which a player can force a win by remaining in the set forever. ...
In order to instantiate a dominion space, we need to define a suitable query function to compute quasi dominions and a successor operator to ensure progress in the search for a closed dominion. ...
doi:10.4204/eptcs.226.3
fatcat:6zagd7zjt5fzdfe4ras7yzhy6e
The Strahler Number of a Parity Game
2020
International Colloquium on Automata, Languages and Programming
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It is shown that the Strahler number of a parity game is a robust, and hence arguably natural, parameter: it coincides with its alternative version based on trees of progress measures and - remarkably ...
The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. ...
Acknowledgements We thank colleagues in the following human chain for contributing to our education on the Strahler number of a tree: the first and the second authors have learnt it from the third author ...
doi:10.4230/lipics.icalp.2020.123
dblp:conf/icalp/DaviaudJT20
fatcat:nklxsmvohne27fd63daygc2kba
Attracting Tangles to Solve Parity Games
[chapter]
2018
Lecture Notes in Computer Science
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They are also interesting from the theory perspective, because they are widely believed to admit a polynomial solution, but so far no such algorithm is known. ...
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. ...
Quasi-polynomial Time Progress Measures The quasi-polynomial time progress measures algorithm [12] is similar to small progress measures. ...
doi:10.1007/978-3-319-96142-2_14
fatcat:4qq7sijjwfck5jxnusrkjiekrm
Solving Parity Games via Priority Promotion
[chapter]
2016
Lecture Notes in Computer Science
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The problem has a rather intriguing status from a complexity theoretic viewpoint, since it belongs to the class UPTime ∩ CoUPTime, and still open is the question whether it can be solved in polynomial ...
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. ...
Our solution to this problem is to proceed in a bottom-up fashion, starting from a weaker notion of α-dominion, called quasi αdominion. ...
doi:10.1007/978-3-319-41540-6_15
fatcat:4wj7uh75wberbfnlzdn6ozypme
Solving parity games via priority promotion
2018
Formal methods in system design
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A quasi dominion Q for player α ∈ {0, 1}, called a quasi α-dominion, is a set of vertices from each ...
To the second family belongs the procedure proposed by Jurdziński [32] , which exploits the connection between the notions of progress measures [35] and winning strategies. ...
Our solution to this problem is to proceed in a bottom-up fashion, starting from a weaker notion of α-dominion, called quasi α-dominion. ...
doi:10.1007/s10703-018-0315-1
fatcat:qb4e5r2lr5fozgtn5p4liiaqy4
The Strahler number of a parity game
[article]
2020
arXiv
pre-print
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It is shown that the Strahler number of a parity game is a robust parameter: it coincides with its alternative version based on trees of progress measures and with the register number defined by Lehtinen ...
The Strahler number of a parity game is proposed to be defined as the smallest Strahler number of the tree of any of its attractor decompositions. ...
H = A, (S 1 , Inductively, for all i, there is a progress measure tree T i (and an associated progress measure mapping µ i ) of the same height as T Hi and an embedding f i from T Hi to T i such that all ...
arXiv:2003.08627v2
fatcat:rbfaswl66fg45nc2ml6ymhe4ki
Priority Promotion with Parysian Flair
[article]
2021
arXiv
pre-print
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We develop an algorithm that combines the advantages of priority promotion - one of the leading approaches to solving large parity games in practice - with the quasi-polynomial time guarantees offered ...
Hybridising these algorithms sounds both natural and difficult, as they both generalise the classic recursive algorithm in different ways that appear to be irreconcilable: while the promotion transcends ...
Acknowledgments This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 101032464. F. ...
arXiv:2105.01738v2
fatcat:m4u76cm3vrfnbiu4flje4swmqa
Page 96 of Republic; A Monthly Magazine Devoted to the Dissemination of Political Information Vol. 2, Issue 2
[page]
1874
Republic; A Monthly Magazine Devoted to the Dissemination of Political Information
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Dominion they have not yet consented to an affiliation. ...
Total. ......... ree Jes
Total exports of Dominion products from British Columbia for the year ended June 30, 1873.
1,767,068
To—
Great Britain....................... $224,924 United States............ ...
A Parity Game Tale of Two Counters
[article]
2018
arXiv
pre-print
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We are the first to provide an exponential lower bound to priority promotion with the delayed promotion policy, and the first to provide such a lower bound to tangle learning. ...
The problem is believed to admit a solution in polynomial time, motivating researchers to find candidates for such an algorithm and to defeat these algorithms. ...
Apart from the earlier described algorithms, we consider the APT algorithm [33] , the small progress measures algorithm [28] (SPM), and we also look at recent quasi-polynomial algorithms, namely the ...
arXiv:1807.10210v2
fatcat:xvo4cmlk3fgbjj74jqw5ur2th4
Parity Games: Zielonka's Algorithm in Quasi-Polynomial Time
2019
International Symposium on Mathematical Foundations of Computer Science
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After this breakthrough result, a few other quasi-polynomial-time algorithms were introduced; none of them is easy to understand. Moreover, it turns out that in practice they operate very slowly. ...
In effect, we obtain a simple algorithm that solves parity games in quasi-polynomial time. ...
Far later, we have the small progress measure algorithm [19] . ...
doi:10.4230/lipics.mfcs.2019.10
dblp:conf/mfcs/Parys19
fatcat:uhmhljxtjjhtfgll7hhmqk5zda
Parity Games: Zielonka's Algorithm in Quasi-Polynomial Time
[article]
2019
arXiv
pre-print
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After this breakthrough result, a few other quasi-polynomial-time algorithms were introduced; none of them is easy to understand. Moreover, it turns out that in practice they operate very slowly. ...
In effect, we obtain a simple algorithm that solves parity games in quasi-polynomial time. ...
Far later, we have the small progress measure algorithm [19] . ...
arXiv:1904.12446v1
fatcat:lzzbu22atneu5fs6her72moesi
Improved Set-based Symbolic Algorithms for Parity Games
[article]
2017
arXiv
pre-print
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Parity conditions are canonical forms to specify ω-regular winning conditions. ...
While many explicit algorithms exist for graph games with parity conditions, for set-based symbolic algorithms there are only two algorithms (notice that we use space to refer to the number of sets stored ...
Strategies from progress measure. ...
arXiv:1706.04889v1
fatcat:ajlksmwyb5adhj3ndxspnvh42q
A Comparison of BDD-Based Parity Game Solvers
2018
Electronic Proceedings in Theoretical Computer Science
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It is therefore important to identify algorithms that can efficiently deal with large games that arise from such applications. ...
We compare their performance on several types of random games and on a number of cases taken from the Keiren benchmark set. ...
small progress measures algorithm, see [8] . ...
doi:10.4204/eptcs.277.8
fatcat:76qxzmcteffbrpxvapewuqgwty
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