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DAG-Width and Parity Games
[chapter]

2006
*
Lecture Notes in Computer Science
*

In particular, we show that the problem of determining the winner of a

doi:10.1007/11672142_43
fatcat:zezwz7kznvaxvha47mpqujapui
*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. ...##
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Time and Parallelizability Results for Parity Games with Bounded Tree and DAG Width

2013
*
Logical Methods in Computer Science
*

In this paper, we study

doi:10.2168/lmcs-9(2:6)2013
fatcat:ec3rkwrzebhv7a3pip5y2agpuq
*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*. ...##
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DAG-width of Control Flow Graphs with Applications to Model Checking
[article]

2015
*
arXiv
*
pre-print

One consequence of this result is that

arXiv:1503.00793v1
fatcat:2ymtppbwkfccrmfvcb3xpu3vsu
*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. ...##
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Alternating Weak Automata from Universal Trees
[article]

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

arXiv:1903.12620v1
fatcat:slqbuf3vbrduvgitwyrm5euxmm
*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 ...##
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Digraph width measures in parameterized algorithmics

2014
*
Discrete Applied Mathematics
*

To this end, we introduce new measures K-

doi:10.1016/j.dam.2013.10.038
fatcat:jw3g26o5gvc7dnk4mhsp2nnmkm
*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. ...##
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The dag-width of directed graphs

2012
*
Journal of combinatorial theory. Series B (Print)
*

In particular, we show that the problem of determining the winner of a

doi:10.1016/j.jctb.2012.04.004
fatcat:d6w5uaykebh7hi3fkqwmnp4czi
*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. ...##
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DAG-width

2006
*
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
*

Fact: Clique of size n has tree-

doi:10.1145/1109557.1109647
fatcat:wksbz7o2nrcspks6xx3abwsyhm
*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. ...##
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Parity Games with Partial Information Played on Graphs of Bounded Complexity
[chapter]

2010
*
Lecture Notes in Computer Science
*

We address the strategy problem for

doi:10.1007/978-3-642-15155-2_53
fatcat:tqi43uqoxzhejeddkdy2bfsaya
*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. ...##
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Decomposition theorems and model-checking for the modalμ-calculus

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-

doi:10.1145/2603088.2603144
dblp:conf/csl/BojanczykDK14
fatcat:vfhrvywtezbvjis7i3mglnqzfq
*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. ...##
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The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs

2014
*
Theoretical Computer Science
*

for

doi:10.1016/j.tcs.2013.12.021
fatcat:wz6dcmxi2jc2ljlintmdmgxe7a
*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 . ...##
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The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs
[article]

2012
*
arXiv
*
pre-print

We analyse the examples provided by Friedmann in terms of complexity measures for directed graphs such as treewidth,

arXiv:1210.2459v1
fatcat:vptg3s37n5d3lnwvlsguo7faem
*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. ...##
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Digraph measures: Kelly decompositions, games, and orderings

2008
*
Theoretical Computer Science
*

We consider various well-known, equivalent complexity measures for graphs such as elimination orderings, k-trees

doi:10.1016/j.tcs.2008.02.038
fatcat:kmiscfo3kvafflb4o66nswgyxa
*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*. ...##
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Parity Games, Imperfect Information and Structural Complexity
[article]

2017
*
arXiv
*
pre-print

Such results are known for graph classes of bounded tree-

arXiv:1703.00683v1
fatcat:k3zefonhondk3dm5lkmp6voyue
*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. ...##
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Entanglement and the complexity of directed graphs

2012
*
Theoretical Computer Science
*

There exist graphs of

doi:10.1016/j.tcs.2012.07.010
fatcat:cd3q3i43arcznefrbk6xmkze3a
*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*. ...##
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The Complexity of Boundedness for Guarded Logics

2015
*
2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science
*

It is known that guarded logics have many desirable computational

doi:10.1109/lics.2015.36
dblp:conf/lics/BenediktCCB15
fatcat:dfty4xxupfgnzb4wjmt3rz4ys4
*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*. ...
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