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DAG-Width and Parity Games [chapter]

Dietmar Berwanger, Anuj Dawar, Paul Hunter, Stephan Kreutzer
2006 Lecture Notes in Computer Science  
In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded DAG-width.  ...  We also consider the relationship between DAG-width and other measures such as entanglement and directed tree-width.  ...  Parity Games on Graphs of Bounded DAG-Width A parity game P is a tuple (V, V 0 , E, Ω) where (V, E) is a directed graph, V 0 ⊆ V and Ω : V → ω is a function assigning a priority to each node.  ... 
doi:10.1007/11672142_43 fatcat:zezwz7kznvaxvha47mpqujapui

Time and Parallelizability Results for Parity Games with Bounded Tree and DAG Width

John Fearnley, Sven Schewe, Erich Grädel
2013 Logical Methods in Computer Science  
In this paper, we study parity games on graphs with bounded treewidth, and graphs with bounded DAG width.  ...  We show that parity games with bounded DAG width can be solved in O(n^(k+3) k^(k + 2) (d + 1)^(3k + 2)) time, where n, k, and d are the size, treewidth, and number of priorities in the parity game.  ...  Our first result is for parity games with bounded DAG width.  ... 
doi:10.2168/lmcs-9(2:6)2013 fatcat:ec3rkwrzebhv7a3pip5y2agpuq

DAG-width of Control Flow Graphs with Applications to Model Checking [article]

Therese Biedl, Sebastian Fischmeister, Neeraj Kumar
2015 arXiv   pre-print
One consequence of this result is that parity games (and hence the μ-calculus model checking problem), which are known to be tractable on graphs of bounded DAG-width, can be solved efficiently in practice  ...  We use the so-called DAG-width and show that the DAG-width of control flow graphs arising from structured (goto-free) programs is at most three.  ...  Section 2 reviews notation and background material, especially the cops and robbers game and its relation to DAG-width. The proof of the DAG-width bound follows in Section 3.  ... 
arXiv:1503.00793v1 fatcat:2ymtppbwkfccrmfvcb3xpu3vsu

Alternating Weak Automata from Universal Trees [article]

Laure Daviaud, Marcin Jurdzinski, Karoliina Lehtinen
2019 arXiv   pre-print
Any slightly better such translation would (if---like all presently known such translations---it is efficiently constructive) lead to algorithms for solving parity games that are asymptotically faster  ...  An improved translation from alternating parity automata on infinite words to alternating weak automata is given.  ...  By positional determinacy of parity games [7] , [21] , Alice has a positional winning strategy in G(B, w), whose strategy subgraph [9] is a layered dag of width at most |Q|, and in which all paths  ... 
arXiv:1903.12620v1 fatcat:slqbuf3vbrduvgitwyrm5euxmm

Digraph width measures in parameterized algorithmics

Robert Ganian, Petr Hliněný, Joachim Kneis, Alexander Langer, Jan Obdržálek, Peter Rossmanith
2014 Discrete Applied Mathematics  
To this end, we introduce new measures K-width and DAGdepth.  ...  We support this direction by showing that many quite different problems remain hard even on graph classes that are restricted very beyond simply having small DAG-width.  ...  This work has been supported by a Czech-German bilateral grant of GAČR and DFG (201/09/J021 and RO 927/9). Moreover, P. Hliněný has been supported by the Czech research grant GAČR 201/08/0308.  ... 
doi:10.1016/j.dam.2013.10.038 fatcat:jw3g26o5gvc7dnk4mhsp2nnmkm

The dag-width of directed graphs

Dietmar Berwanger, Anuj Dawar, Paul Hunter, Stephan Kreutzer, Jan Obdržálek
2012 Journal of combinatorial theory. Series B (Print)  
In particular, we show that the problem of determining the winner of a parity game is solvable in polynomial time on graphs of bounded dag-width.  ...  We also consider the relationship between dag-width and other connectivity measures such as directed tree-width and path-width.  ...  Acknowledgments This work has been partially supported by the ESF Networking Programme GAMES and the Czech research grant GAČR 201/09/J021.  ... 
doi:10.1016/j.jctb.2012.04.004 fatcat:d6w5uaykebh7hi3fkqwmnp4czi

DAG-width

Jan Obdržálek
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
Fact: Clique of size n has tree-width n. Here is a DAG with n vertices and tree-width n (for n = 5): But it is easy to solve parity games on DAGs!  ...  Directed Tree-width -an example a b c d a bc d [b] [c] SODA'06 Directed Tree-width -the game Essentially the same "cops and robber" game as for tree-width, with the following two restrictions on robber  ...  • parity games Note: In the case of tree-width the algorithms usually run in linear time.  ... 
doi:10.1145/1109557.1109647 fatcat:wksbz7o2nrcspks6xx3abwsyhm

Parity Games with Partial Information Played on Graphs of Bounded Complexity [chapter]

Bernd Puchala, Roman Rabinovich
2010 Lecture Notes in Computer Science  
We address the strategy problem for parity games with partial information and observable colors, played on finite graphs of bounded complexity.  ...  Hence, parity games with bounded partial information, played on graphs with bounded directed path-width can be solved in polynomial time.  ...  DAG-width, introduced in [2, 13] , is defined via the cops and directed visible robber game (DAG-width game, for short). The DAG-width game on a graph G = (V, E) is defined as follows.  ... 
doi:10.1007/978-3-642-15155-2_53 fatcat:tqi43uqoxzhejeddkdy2bfsaya

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  
As a consequence we show that the model-checking problem for L_μ is fixed-parameter tractable (fpt) on classes of structures of bounded Kelly-width or bounded DAG-width.  ...  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.  ...  DAG-width and Kelly-width are as yet uncomparable concepts.  ... 
doi:10.1145/2603088.2603144 dblp:conf/csl/BojanczykDK14 fatcat:vfhrvywtezbvjis7i3mglnqzfq

The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs

Felix Canavoi, Erich Grädel, Roman Rabinovich
2014 Theoretical Computer Science  
for DAG-width and Kelly-width, or as a parse tree for cliquewidth.  ...  These include parity games of bounded treewidth [15] , bounded entanglement [3, 4] , bounded DAG-width [2] , bounded Kelly-width [10] , or bounded cliquewidth [16] .  ...  connecting K → K and K → K. Thus the conncections between L i+1 and the previous layers have been established. Next, we construct the rest of L i+1 using colours C, Done, B, D, H l and H r .  ... 
doi:10.1016/j.tcs.2013.12.021 fatcat:wz6dcmxi2jc2ljlintmdmgxe7a

The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs [article]

Felix Canavoi, Erich Grädel, Roman Rabinovich
2012 arXiv   pre-print
We analyse the examples provided by Friedmann in terms of complexity measures for directed graphs such as treewidth, DAG-width, Kelly-width, entanglement, directed pathwidth, and cliquewidth.  ...  For some time the discrete strategy improvement algorithm due to Jurdzinski and Voge had been considered as a candidate for solving parity games in polynomial time.  ...  Then the winning regions of parity games on C are computable in polynomial time. It follows directly from the definitions that DAG-width and Kelly-width are bounded in directed pathwidth.  ... 
arXiv:1210.2459v1 fatcat:vptg3s37n5d3lnwvlsguo7faem

Digraph measures: Kelly decompositions, games, and orderings

Paul Hunter, Stephan Kreutzer
2008 Theoretical Computer Science  
We consider various well-known, equivalent complexity measures for graphs such as elimination orderings, k-trees and cops and robber games and study their natural translations to digraphs.  ...  We introduce a decomposition for digraphs and an associated width, Kelly-width, which is equivalent to the aforementioned measure.  ...  Parity Games. Another example for an algorithm on graphs of bounded Kelly-width is an algorithm for solving parity games on game arenas of small Kelly-width.  ... 
doi:10.1016/j.tcs.2008.02.038 fatcat:kmiscfo3kvafflb4o66nswgyxa

Parity Games, Imperfect Information and Structural Complexity [article]

Bernd Puchala, Roman Rabinovich
2017 arXiv   pre-print
Such results are known for graph classes of bounded tree-width, DAG-width, directed path-width, and entanglement, which we describe in terms of cops and robber games.  ...  Hence, if directed path-width or DAG-width are bounded, parity games with bounded imperfect information can be solved in PTIME. For DAG-width we follow two approaches.  ...  We thank Lukasz Kaiser for many inspiring discussions, Tsvetelina Yonova-Karbe and Sebastian Siebertz for the proof reading.  ... 
arXiv:1703.00683v1 fatcat:k3zefonhondk3dm5lkmp6voyue

Entanglement and the complexity of directed graphs

Dietmar Berwanger, Erich Grädel, Łukasz Kaiser, Roman Rabinovich
2012 Theoretical Computer Science  
There exist graphs of DAG-width, Kelly-width and directed treewidth three and arbitrarily large entanglement.  ...  Furthermore, parity games can be solved efficiently on game graphs of bounded  ...  Acknowledgments This work has been partially supported by the ESF Networking Programme GAMES.  ... 
doi:10.1016/j.tcs.2012.07.010 fatcat:cd3q3i43arcznefrbk6xmkze3a

The Complexity of Boundedness for Guarded Logics

Michael Benedikt, Balder Ten Cate, Thomas Colcombet, Michael Vanden Boom
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
It is known that guarded logics have many desirable computational and model theoretic properties, including in some cases decidable boundedness.  ...  We prove that boundedness for the guarded negation fragment is decidable in elementary time, and, making use of an unpublished result of Colcombet, even 2EXPTIME-complete.  ...  We now transform the S∧parity game into a B ∧ parity game.  ... 
doi:10.1109/lics.2015.36 dblp:conf/lics/BenediktCCB15 fatcat:dfty4xxupfgnzb4wjmt3rz4ys4
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