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From Quasi-Dominions to Progress Measures [article]

Massimo Benerecetti, Daniele Dell'Erba, Marco Faella, Fabio Mogavero
2021 arXiv   pre-print
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]

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2020 Lecture Notes in Computer Science  
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

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2016 Electronic Proceedings in Theoretical Computer Science  
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

Laure Daviaud, Marcin Jurdziński, K. S. Thejaswini, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
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]

Tom van Dijk
2018 Lecture Notes in Computer Science  
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]

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2016 Lecture Notes in Computer Science  
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

Massimo Benerecetti, Daniele Dell'Erba, Fabio Mogavero
2018 Formal methods in system design  
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]

Laure Daviaud and Marcin Jurdziński and K. S. Thejaswini
2020 arXiv   pre-print
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]

Massimo Benerecetti
2021 arXiv   pre-print
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  
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]

Tom van Dijk
2018 arXiv   pre-print
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

Pawel Parys, Michael Wagner
2019 International Symposium on Mathematical Foundations of Computer Science  
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]

Paweł Parys
2019 arXiv   pre-print
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]

Krishnendu Chatterjee and Wolfgang Dvořák and Monika Henzinger and Veronika Loitzenbauer
2017 arXiv   pre-print
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

Lisette Sanchez, Wieger Wesselink, Tim A.C. Willemse
2018 Electronic Proceedings in Theoretical Computer Science  
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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