J. R. Buchi. Using determinacy to eliminate quantifiers. Lecture Notes in Computer Science, 56, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....s.t. A accepts the Sigma 1 Theta Sigma 2 labelled tree given by (w) 1 (w) 2 (w) for all w 2 f0; 1g . 40 Tree Automata as Games We outline (part of) a proof of the expressive equivalence of S2S and the Rabin recognisable languages based on games. This approach is due to Buchi [5, 6] and Gurevich and Harrington [23] We follow here Gurevich [22] Definition 40.1 (Game automata) A game automaton (a tree automaton in [22] but we have already used that term) is a structure A g = S; f g i2f0;1g;a2 Sigma ; f in g a2 Sigma ; F ) where 1. S is a finite set of ....

J. R. Buchi. Using determinacy to eliminate quantifiers. Lecture Notes in Computer Science, 56, 1977.

....s.t. A accepts the Sigma 1 Theta Sigma 2 labelled tree given by (w) 1 (w) 2 (w) for all w 2 f0; 1g . 40 Tree Automata as Games We outline (part of) a proof of the expressive equivalence of S2S and the Rabin recognisable languages based on games. This approach is due to Buchi [5, 6] and Gurevich and Harrington [23] We follow here Gurevich [22] Definition 40.1 (Game automata) A game automaton (a tree automaton in [22] but we have already used that term) is a structure A g = S; f (i;a) g i2f0;1g;a2 Sigma ; f a in g a2 Sigma ; F ) where 1. S is a finite set of ....

J. R. Buchi. Using determinacy to eliminate quantifiers. Lecture Notes in Computer Science, 56, 1977.

....theory) For example, by means of states, periodicities in plays may be immediately captured by state repetitions, and also different potentials of performing actions (depending on the momentary state) are simply describable. In the following we introduce state based games, using terminology from [Bu77], Bu83] GH82] McN93] and [Ze94] A game graph is of the form G = Q; Q 0 ; Q 1 ; A; ffi; Omega ) where Q is a finite or countable set of states , Q 0 ; Q 1 define a partition of Q (Q i containing the states where it is the turn of player i to perform an action) A is a finite set (of ....

....By lack of space we cannot enter this interesting subject here. For example, fixed point constructions (as above in Section 3.1 for the finite state case) require now ordinal indexed sets. Games of this form can be applied to obtain the complementation of Rabin tree automata (as proposed by Buchi [Bu77], Bu83] Several approaches have been developed to obtain transparent proofs; as recent references, besides the papers listed above, we mention [EJ91] Mu92] Kl94] MS94] 4 Games over pushdown transition graphs and recursive graphs The subject of this section is still in its beginnings: ....

J.R. Buchi, Using determinacy to eliminate quantifiers, in: Fundamentals of Computation Theory (M. Karpinski, ed.), Lecture Notes in Computer Science 56, Springer-Verlag, Berlin 1977, pp. 367-378.

....and obtained applications in several areas. The core of Rabin s work is a complementation theorem for nondeterministic finite automata on infinite trees. In the first two parts of this section we give a fairly self contained proof, which follows a game theoretical approach suggested by Buchi [Bu77], Bu83] and Gurevich and Harrington [GH82] and uses more recent work of [EJ91] Mst91a] McN93] Th95] and [Zie95] The last section presents some logical applications. 6.1 Automata on Infinite Trees We shall consider finite tree automata working top down on infinite input trees. ....

J.R. Buchi, Using determinacy to eliminate quantifiers, in: Fundamentals of Computation Theory (M. Karpinski, Ed.), Lecture Notes in Computer Science 56, Springer-Verlag, Berlin 1977, pp. 367-378.

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