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Page 6548 of Mathematical Reviews Vol. , Issue 87k [page]

1987 Mathematical Reviews  
Andrea Maggiolo-Schettini (Pisa) COMPUTER SCIENCE 6548 Muller, David (1-IL); Schupp, Paul E. (1-IL) Alternating automata on infinite objects. Determinacy and Rabin’s theorem.  ...  It is not im- mediately obvious that the alternating automata which we define are equivalent to ordinary nondeterministic automata on infinite trees.  ... 

How unprovable is Rabin's decidability theorem? [article]

Leszek Aleksander Kołodziejczyk, Henryk Michalewski
2015 arXiv   pre-print
We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree.  ...  the infinite binary tree, positional determinacy of parity games and determinacy of Bool(Σ^0_2) Gale-Stewart games are all equivalent.  ...  We first focus our attention on the complementation theorem for automata on infinite trees, which is the key ingredient in typical proofs of Rabin's theorem and is often simply considered an alternative  ... 
arXiv:1508.06780v1 fatcat:3c55nyrbvrb4vhq6ectcwjizh4

Facets of Synthesis: Revisiting Church's Problem [chapter]

Wolfgang Thomas
2009 Lecture Notes in Computer Science  
We outline the methodology developed in more recent years for solving such games and address related automata theoretic problems that are still unresolved.  ...  We recall the fundamental questions raised more than 50 years ago in "Church's Synthesis Problem" that led to the foundation of the algorithmic theory of infinite games.  ...  Tree Automata A very strong decidability result of logic is Rabin's Tree Theorem, saying that the MSO-theory of the infinite binary tree is decidable [21] .  ... 
doi:10.1007/978-3-642-00596-1_1 fatcat:uhny7wacofafzl3s4fcd6sc37e

Page 3748 of Mathematical Reviews Vol. , Issue 86h [page]

1986 Mathematical Reviews  
Determinacy and Rabin’s theorem (pp. 100-107); J. P. Braquelaire and B.  ...  Shields, Deterministic asynchronous automata (pp. 89-98). Part III. Automata on infinite trees: David Muller and Paul E. Schupp, Alternating automata on infinite objects.  ... 

Progress measures, immediate determinacy, and a subset construction for tree automata

Nils Klarlund
1994 Annals of Pure and Applied Logic  
To do this we show that for certain infinite games based on tree automata, an immediate determinacy property holds for the player who is trying to win according to a Rabin acceptance condition.  ...  Together, these ingredients and the determinacy of Bore1 games yield a straightforward recipe for complementing tree automata.  ...  Acknowledgements Thanks are due to Charanjit Jutla for motivating discussions and to Suzanne Zeitman for extraordinary insightful and useful comments.  ... 
doi:10.1016/0168-0072(94)90086-8 fatcat:tpyxgkzjhreulfqcuespcnzlgi

Determinization and Memoryless Winning Strategies

Charanjit S. Jutla
1997 Information and Computation  
As mentioned earlier, the main difference between automata on infinite objects and automata on finite objects is the way acceptance is defined.  ...  AUTOMATA ON INFINITE STRINGS We begin by studying automata on infinite strings (also called |-automata), because most constructions for automata on infinite trees use constructions for |-automata as a  ... 
doi:10.1006/inco.1997.2624 fatcat:slk3zgykejg23i5knm6zr5iho4

An Optimal Value Iteration Algorithm for Parity Games [article]

Nathanaël Fijalkow
2018 arXiv   pre-print
In this paper, we further analyse the second algorithm due to Jurdzi\'nski and Lazi\'c and called the succinct progress measure algorithm.  ...  This suggests that the succinct progress measure algorithm of Jurdzi\'nski and Lazi\'c is in this framework optimal, and that the polynomial time algorithm for parity games is hiding someplace else.  ...  on lower bounds for universal trees, and Élie de Panafieu for his expertise on combinatorial analysis.  ... 
arXiv:1801.09618v1 fatcat:sknboutetjakvaskzucyxsh64q

Trading Bounds for Memory in Games with Counters [chapter]

Nathanaël Fijalkow, Florian Horn, Denis Kuperberg, Michał Skrzypczak
2015 Lecture Notes in Computer Science  
The games we consider are played by two players, Eve and Adam, over potentially infinite graphs called arenas 4 .  ...  We investigate the existence of a trade-off between the size of the memory and the bound achieved on the counters, which has been conjectured by Colcombet and Löding.  ...  The unbounded number of fruitful discussions we had with Thomas Colcombet and Miko laj Bojańczyk made this paper possible.  ... 
doi:10.1007/978-3-662-47666-6_16 fatcat:rdmlydtlr5e2zhf4wylo6gtuq4

An initial semantics for the μ-calculus on trees and Rabin's complementation lemma

André Arnold
1995 Theoretical Computer Science  
In this paper we show that the function associated with any closed or nonclosed term of the /I-calculus on trees can be represented by a recognizable set of trees whose nodes arc labeled by letters and  ...  Rabin's complementation lemma is an immediate consequence of this result.  ...  Niwiriski, and an anonymous referee for carefully reading this text and for their numerous comments, remarks and suggestions.  ... 
doi:10.1016/0304-3975(95)00069-9 fatcat:5f4cg2uynrexxoiaxlw76m3jsq

A Functional (Monadic) Second-Order Theory of Infinite Trees [article]

Anupam Das, Colin Riba
2020 arXiv   pre-print
MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results concerning the decidability of logics.  ...  By naive enumeration of formal derivations, this formally gives a proof of Rabin's Tree Theorem.  ...  Rabin's Tree Theorem [Rab69] , the decidability of MSO on infinite trees, is one of the most powerful known results concerning the decidability of logics (see e.g. [BGG97] ).  ... 
arXiv:1903.05878v3 fatcat:y2sdsucbvbhdpjm4lyj4tqjjma

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

Wieslaw Zielonka
1998 Theoretical Computer Science  
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.  ...  Based on a previous work of Gurevich and Harrington and on subsequent improvements of McNaughton we propose a unique framework that allows to reestablish and to improve various results concerning memoryless  ...  All three conditions defined above are frequently used as acceptance conditions for automata on infinite objects.  ... 
doi:10.1016/s0304-3975(98)00009-7 fatcat:emqhjo524vbh7dtw74gf4ix6vq

Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra

David E. Muller, Paul E. Schupp
1995 Theoretical Computer Science  
We give a proof that alternating tree automata can be simulated by nondeterministic tree automata which yields new complexity results and a unified proof of the theorems of Rabin, McNaughton and Safra.  ...  Zeitman and another referee for helpful comments on this paper.  ...  Appendix C reviews some essential notation and results concerning alternating automata on infinite trees, including the Logical Equivalence Theorem showing that the properties of an alternating automaton  ... 
doi:10.1016/0304-3975(94)00214-4 fatcat:n7hnq27g5nbbdlmf6y4762l644

A Functional (Monadic) Second-Order Theory of Infinite Trees

Anupam Das, Colin Riba
2019 Logical Methods in Computer Science  
MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree Theorem") is one of the most powerful known results concerning the decidability of logics.  ...  By naive enumeration of formal derivations, this formally gives a proof of Rabin's Tree Theorem.  ...  Rabin's Tree Theorem [Rab69] , the decidability of MSO on infinite trees, is one of the most powerful known results concerning the decidability of logics (see e.g. [BGG97] ).  ... 
doi:10.23638/lmcs-16(4:6)2020 fatcat:vdekrc4qwzaoleebdauabxcqiu

Alternating automata on infinite trees

David E. Muller, Paul E. Schupp
1987 Theoretical Computer Science  
See Lindsay [7, 8] and Miyano and Hayashi [lo] . Alter We consider the theory of alternating automata on the infinite k-ary tree, k a 1.  ...  Both finite state automata and Turing machines which are alternating is the sense of Chandra, Kozen and Stockmeyer ha ve been considered on infinite words.  ...  Schupp successive values of n one can sekect a minimal choice set among the histories chosen by fl in ~;WA A a way that the minimal choice set selected at stage n -1 is extended.  ... 
doi:10.1016/0304-3975(87)90133-2 fatcat:kji3bzn6ijbirakvrweqzcxfkm

From Logic to Games [chapter]

Igor Walukiewicz
2005 Lecture Notes in Computer Science  
Independently, Büchi [17] , and Gurevich and Harrington [40] , arrive at understanding that the cornerstone of Rabin's decidability result for MSO theory of trees is a theorem about existence of some  ...  Alternating Automata An alternating automaton on on transition systems is a tuple: A = A, P, Q ∃ , Q ∀ , q 0 , δ : Q × P(P ) → P(A × Q), Acc where A ⊆ Act ∪ {id }, P ⊆ Prop are finite set of actions and  ... 
doi:10.1007/11590156_5 fatcat:ps3dhgrvcnhabi6432n2rm5qrm
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