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Infinite games on finitely coloured graphs with applications to automata on infinite trees

Wieslaw Zielonka
1998 Theoretical Computer Science  
We examine a class of infinite two-person games on finitely coloured graphs. The main aim is to construct finite memory winning strategies for both players.  ...  This problem is motivated by applications to finite automata on infinite trees. A special attention is given to the exact amount of memory needed by the players for their winning strategies.  ...  The graphs used as game arenas can be either finite or infinite, in fact the major application of these games -the complementation lemma for automata on infinite trees -involves games on infinite graphs  ... 
doi:10.1016/s0304-3975(98)00009-7 fatcat:emqhjo524vbh7dtw74gf4ix6vq

Author index volume 200 (1998)

1998 Theoretical Computer Science  
., Operational semantics of rewriting with priorities Zielonka, W., Infinite games on finitely coloured graphs with applications to automata on infinite trees(Fundamental Study)  ...  ., Stable trace automata vs. full trace automata (Fundamental Study)Stinson, D.R., see C.  ... 
doi:10.1016/s0304-3975(98)00113-3 fatcat:pmlmy6qbezg7xhxx2z2nza35vy

From Logic to Games [chapter]

Igor Walukiewicz
2005 Lecture Notes in Computer Science  
If we permit partial assignments of colours or put coloring on edges of the game graph and not on positions then only ordinary (i.e. finite) parity conditions admit memoryless strategies [26] .  ...  In most of the cases here the winning conditions Acc ⊆ V ω will be Muller conditions: that is, there will be a colouring λ : V → Colours of the set of vertices with a finite set of colours and a set F  ... 
doi:10.1007/11590156_5 fatcat:ps3dhgrvcnhabi6432n2rm5qrm

Page 1440 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
games on finitely coloured graphs with applications to automata on infinite trees.  ...  A class of infinite two-person games on finitely coloured oriented graphs is studied.  ... 

Page 6360 of Mathematical Reviews Vol. , Issue 89K [page]

1989 Mathematical Reviews  
original information.” 89k:68114 68Q99 08A30 Stomiriski, Jézef (PL-TORN) Relative cogenerations with applications to tree automata and a theory of abstract algebras with feedback modifications.  ...  to the characteristics of an infinite automaton with a similar structure is proved.  ... 

Winning Regions of Higher-Order Pushdown Games

Arnaud Carayol, Matthew Hague, Antoine Meyer, C.-H. Luke Ong, Olivier Serre
2008 Logic in Computer Science  
From our main result on winning regions of parity games we derive a solution to the Modal Mu-Calculus Global Model-Checking Problem for higher-order pushdown graphs as well as for ranked trees generated  ...  A novelty of our work are abstract pushdown processes which can be seen as (ordinary) pushdown automata but with an infinite stack alphabet.  ...  Starting with an order-n pushdown parity game, and applying n times the reduction of Proposition 1, one ends up with a parity game using the same number of colours over a finite game graph whose size,  ... 
doi:10.1109/lics.2008.41 dblp:conf/lics/CarayolHMOS08 fatcat:lgkwjeewtzgvfcfpqan5dyckji

Automata on Directed Graphs: Edge Versus Vertex Marking [chapter]

Dietmar Berwanger, David Janin
2006 Lecture Notes in Computer Science  
We investigate two models of finite-state automata that operate on rooted directed graphs by marking either vertices (V-automata) or edges (E-automata).  ...  Our main result implies that every MSOdefinable tree language can be recognised by E-automata with uniform runs, that is, runs that do not distinguish between isomorphic subtrees.  ...  Whenever we speak of a Σ-coloured graph, we mean a graph with a vertex colouring over a finite alphabet Σ. Definition 1 (V-automaton). Let Σ be a finite alphabet of vertex colours.  ... 
doi:10.1007/11841883_5 fatcat:p3docobnardtde53mbv5wszdsa

The Theory of Universal Graphs for Infinite Duration Games [article]

Thomas Colcombet, Nathanaël Fijalkow, Paweł Gawrychowski, Pierre Ohlmann
2022 arXiv   pre-print
In the second part we give four applications: to parity games, to mean payoff games, and to combinations of them (in the form of disjunctions of objectives).  ...  We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games.  ...  Let us start with reviewing the recent results on parity games and their relationships with separating automata, GFSG automata, and universal trees.  ... 
arXiv:2104.05262v5 fatcat:vqn5zmzp55czlougghfsihj3b4

New Algorithms for Combinations of Objectives using Separating Automata

Ashwani Anand, Nathanaël Fijalkow, Aliénor Goubault-Larrecq, Jérôme Leroux, Pierre Ohlmann
2021 Electronic Proceedings in Theoretical Computer Science  
In this paper we show that separating automata is a powerful tool for constructing algorithms solving games with combinations of objectives.  ...  The notion of separating automata was introduced by Bojanczyk and Czerwinski for understanding the first quasipolynomial time algorithm for parity games.  ...  Graphs Graphs We consider edge labelled directed graphs: a graph G is given by a (finite) set V of vertices and a (finite) set E ⊆ V × C × V of edges, with C a set of colours, so we write G = (V, E).  ... 
doi:10.4204/eptcs.346.15 fatcat:ydvst76cf5cq3bos6w5swvqwvm

Counting branches in trees using games

Arnaud Carayol, Olivier Serre
2017 Information and Computation  
We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting.  ...  In all situations we provide a simple acceptance game that later permits to prove that the languages accepted by automata with cardinality constraints are always ω-regular.  ...  Acknowledgement We would like to thanks the anonymous reviewers for their valuable comments, as well as Axel Haddad for his contributions on a preliminary version of this work.  ... 
doi:10.1016/j.ic.2016.11.005 fatcat:hk5mbamj5vblfkddok6fwfljje

Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2021 ACM Transactions on Computational Logic  
This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible  ...  This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes.  ...  A parity game is a game of the form G = (G, Ω ) for some colouring function. Tree Automata We now introduce the usual model of automata to recognise languages of (possibly infinite) ranked trees.  ... 
doi:10.1145/3452917 fatcat:e7pseftknfcxzdwunjwrk6ofkm

Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties [article]

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2021 arXiv   pre-print
This is obtained thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible  ...  This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes.  ...  A parity game is a game of the form G = (G, Ω ) for some colouring function. Tree Automata We now introduce the usual model of automata to recognise languages of (possibly infinite) ranked trees.  ... 
arXiv:2010.06366v2 fatcat:htqiqtp3rfaxxattbycq4hlhsq

Counting Branches in Trees Using Games [article]

Arnaud Carayol, Axel Haddad, Olivier Serre
2015 arXiv   pre-print
We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting.  ...  In all situations we provide a simple acceptance game that later permits to prove that the languages accepted by automata with cardinality constraints are always ω-regular.  ...  Hence, the emptiness problem for tree automata can be reduced to solving a two-player parity game played on a finite graph.  ... 
arXiv:1505.03852v1 fatcat:75ka65bvw5gxhpbavalbces55m

Collapsible Pushdown Parity Games [article]

Christopher H. Broadbent, Arnaud Carayol, Matthew Hague, Andrzej S. Murawski, C.-H. Luke Ong, Olivier Serre
2020 arXiv   pre-print
This paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata.  ...  The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite  ...  one to consider games played on infinite graphs (and the more general the trees, the more general the graphs to be considered).  ... 
arXiv:2010.06361v1 fatcat:zit3yx6ti5bvljehpympuwklka

On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions [article]

Antonio Casares
2021 arXiv   pre-print
Our second contribution concerns the memory requirements of games over graphs using Muller conditions.  ...  In this paper, we relate the problem of determining the chromatic memory requirements of Muller conditions with the minimisation of transition-based Rabin automata.  ...  Acknowledgements I would like to thank Alexandre Blanché for pointing me to the chromatic number problem. I also want to thank Bader Abu Radi, Thomas Colcombet,  ... 
arXiv:2105.12009v3 fatcat:53zbdhisnnathi2f74kdv4ke5u
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