Doner, J. 1970. "Tree Acceptors and some of their Applications". Journal of Computer and System Sciences 4, 406--451.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of several (uniform) membership problems for recognizable tree languages. Furthermore we show that the word problem for a xed nitely presented algebra is in . 1 Introduction Tree automata are a natural generalization of usual word automata to terms. Tree automata were introduced in [11, 12] and [27] in order to solve certain decision problems in logic. Since then they were successfully applied to many other decision problems in logic and term rewriting, see e.g. 7] These applications motivate the investigation of decision problems for tree automata like emptiness, equivalence, and ....

J. E. Doner. Tree acceptors and some of their applications. Journal of Computer and System Sciences, 4:406-451, 1970.

....same set of nite trees up to the projection on the former label domain L. We have preserved the expressivity of the formalisms visited by extending the domain of labels. In contrast to the transformation from monadic second order logic into context free grammars provided by Rabin [20] and Doner [9], our method deals with arbitrary branching trees and performs more transparent and direct alterations. Therefore, we can investigate the expressivity of single principles and the relationship among principles with respect to the described set. Moreover, the resulting (extended) context free ....

Doner, J. (1970), Tree acceptors and some of their applications. Journal of Computer and System Science 4:406-451.

.... For example, the decidability of the (weak) monadic second order logic of one successor (W)S1S was proved by a translation of formulas to word automata [6, 7, 12, 31] and the decidability of the (weak) monadic second order logic on binary trees (W)S2S was shown by a translation to tree automata [9, 24, 29]. Despite the staggering, non elementary, worst case complexity of these decision procedures [21, 28] it was through the Mona tool [10, 14] that it became possible to make e ective use of automatabased decision procedures for WS1S and WS2S for modeling and reasoning about computation systems such ....

J. Doner, Tree acceptors and some of their applications, Journal of Computer and System Sciences, 4 (1970), pp. 406-451.

.... Most prominently, decidability of the (weak) monadic second order logic of one successor (W)S1S is proved by a translation of formulas to word automata [5, 6, 11, 33] and decidability of the (weak) monadic second order logic on binary trees (W)S2S can be shown by a translation to tree automata [9, 26, 31]. Despite the non elementary worst case complexity [22, 30] these automata based decision procedures for WS1S and WS2S have been found to be e ective for reasoning about a multitude of computation systems ranging from sequential circuits [2,3] and imperative programs A preliminary version has ....

J. Doner, Tree acceptors and some of their applications, JCSS, 4 (1970), pp. 406{ 451.

....to the subset relation on the defined sets of feature trees. We are curious to extend the developed theory in the following ways. First, we would like to find a logical characterization of the class of recognizable feature trees, extending the results of Doner, Thatcher Wright and Courcelle [Don70, TW67, Cou90]. It will be interesting to combine second order logic and the counting constraints introduced here, in order to account for the flexibility in the depth as well as in the out degree of the nodes of feature trees. Also, in order to account for circular data structures, like, e.g. circular lists, ....

John E. Doner. Tree Acceptors and some of their applications. Journal of Comp. System Sci. 4, pages 406-451, 1970.

....a general approach which is based on reduction to second order 3 monadic logics, WS2S for finite feature trees and S2S for infinite feature trees. The decidability of WS2S is well known and follows from a classical reduction to the emptiness problem of tree automata [Thatcher Wright, 1968, Doner, 1970, Gecseg Steinby, 1984, Comon et al. 1998] The decidability of S2S is a classical consequence of Rabin s famous theorem on automata for infinite trees [Rabin, 1969, Thomas, 1990, Thomas, 1997] We express feature constraints in second order monadic logic according to a wellknown idea: we ....

....semantics: 9py; 9xy; y y ; y y The second order monadic logic with two successors, S2S and WS2S, are obtained for k = 2. It is well known that (W)SkS can be expressed in (W)S2S for all 2 k w [Thatcher Wright, 1968, Rabin, 1969] Theorem 4. 1 [Rabin, 1969, Thatcher Wright, 1968, Doner, 1970] The satisfiability problems of WS2S and S2S are decidable. 4.1 Relation to Feature Logics Theorem 4.2 The first order theories of FT and FT can be embedded in linear time into S2S and WS2S respectively, and vice versa. In other words, second order monadic logic and the first order ....

J. Doner. Tree acceptors and some of their applications. Journal of Computing Systems Science, 4:406--451, 1970.

....then we dene t T to be the term in T (F) uniquely determined by Pos(t) T and root(t jp ) f if p 2 T f , for all p 2 T . A subset L of T (F) is called WSkS denable if there exists a WSkS formula OE with free variables X such that L = ft T j term( T) OE( T)g. Theorem 2. 7 (Doner [6], Thatcher and Wright [17] A set L T (F) is WSkS denable if and only if it is recognizable. 3 Decidable Approximations of Neededness In the remaining part of the paper we are dealing with nite TRSs only. Moreover, we consider rewriting on ground terms only. So we assume that the set of ground ....

J. Doner, Tree Acceptors and Some of Their Applications, JCSS 4, pp. 406451, 1970.

....of the class of ranked tree automata to the class of unranked tree automata. 4. 3 Expressiveness and complexity As enc and dec are MSO definable, Proposition 1 implies that the famous DonerThatcher Wright characterization of ranked tree automata easily carries over to unranked trees [17, 56]. Corollary 1. 43] A set of trees L is regular i# there is an MSO formula # such that L = t # . Although Proposition 1 provides a tool for transferring results from ranked to unranked trees, it does not deal with issues which are specific for unranked tree automata. The complexity of ....

J. Doner. Tree acceptors and some of their applications. Journal of Computer and System Sciences, 4:406--451, 1970.

....and hence its decision problem is undecidable [99] Theorem 2.2.5 MSOP [ 2] over infinite sequences is undecidable. Moving to trees, MSOP [ pre , # i ) i=0 ] over infinite k ary trees is well known as SkS. The decidability of MSOP [ pre , # i ) over finite trees has been shown in [28, 113]. The decidability of S2S has been proved in [107] This result can be easily generalized to SkS over k ary trees (and even to S#S over countably branching trees) 114] i=0 ] over finite (resp. infinite) trees is decidable. As for layered structures, the decidability of the second order ....

....if there is a run # of A on t such that #(#) finite trees accepted by A. Finite k ary tree automata, for k 2, are defined similarly. Let k be the class of finite k ary tree automata. Finite tree automata are e#ectively closed under Boolean operations and are decidable in polynomial time [28, 113]. Moreover, by exploiting a subset construction , a nondeterministic bottom up finite tree automaton can be converted into a deterministic one accepting the same language. The size of the resulting automaton is exponential in the size of the input automaton. Infinite tree automata are defined as ....

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J. E. Doner. Tree acceptors and some of their applications. Journal of Computer and System Sciences, 4:406--451, 1970.

....5 in which the intersection automaton s size is the product of the sizes of its components) Deduce from the above result that the intersection non emptiness problem for at automata is in NP (compare with Theorem 12) 1. 9 Bibliographic Notes Tree automata were introduced by Doner [Don65, Don70] and Thatcher and Wright [TW65, TW68] Their goal was to prove the decidability of the weak second order theory of multiple successors. The original de nitions are based on the algebraic approach and involve heavy use of universal algebra and or category theory. Many of the basic results ....

J. E. Doner. Tree acceptors and some of their applications. Journal of Comput. and Syst. Sci., 4:406451, 1970.

....of T to an element of . labeled trees are often referred to as trees, and if = T ; V ) is a (labeled) tree and g is a node of T , we use (g) to denote V (g) Two way alternating tree automata (2ATAs) 35, 23] are a generalization of standard nondeterministic top down tree automata (1NTAs) [38, 39]) with both upward moves and with alternation. Let B(I) be the set of positive Boolean formulae over I , built inductively by applying and starting from true, false, and elements of I . For a set J I and a formula 2 B(I) we say that J satis es if and only if, assigning true to the ....

....that T (A[ T (A 1 ) T (An ) We make also use of the following standard results for 1NTAs. Proposition 3 ( 40] Given 1NTAs A 1 and A 2 over an alphabet , there is a 1NTA A of size polynomial in the size of A 1 and A 2 such that T (A ) T (A 1 ) T (A 2 ) Proposition 4 ([38, 39]) The nonemptiness problem for 1NTAs is decidable in polynomial time. 5 Containment of Datalog in Unions of C2RPQs The main feature of proof trees is the fact that the number of possible labels is nite; it is actually exponential in the size of . Because the set of labels is nite, the set of ....

Doner, J.E.: Tree acceptors and some of their applications. J. of Computer and System Sciences 4 (1970) 406-451

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Doner, J. 1970. "Tree Acceptors and some of their Applications". Journal of Computer and System Sciences 4, 406--451.

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J. Doner. Tree acceptors and some of their applications. Journal of Computer and System Sciences, 4:406-451, 1970. 9

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J. Doner. Tree acceptors and some of their applications. J. of Comp. Syst. Sci., 4:406--451, 1970.

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J. Doner. "Tree Acceptors and some of their Applications". Journal of Computer and System Sciences, 4:406--451, 1970.

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J. DONER, Tree acceptors and some of their applications, Journal of Computer and System Sciences, 4 (1970), pp. 406--451. Academic Press.

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J. Doner. "Tree Acceptors and some of their Applications ". Journal of Computer and System Sciences, 4:406-- 451, 1970.

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J. Doner. "Tree Acceptors and some of their Applications ". Journal of Computer and System Sciences, 4:406--451, 1970.

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J. Doner. Tree acceptors and some of their applications. J. Comput. Syst. Sci., 4:405--451, 1970.

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Doner, J. E., Tree acceptors and some of their applications, J. Comput. System Sci. 4 (1970), pp. 406--451.

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J. E. Doner. Tree acceptors and some of their applications. Journal of Comput. and Syst. Sci., 4:406451, 1970.

No context found.

J. E. Doner. Tree acceptors and some of their applications. Journal of Comput. and Syst. Sci., 4:406451, 1970.

No context found.

J. E. Doner. Tree acceptors and some of their applications. Journal of Comput. and Syst. Sci., 4:406451, 1970.

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J. E. Doner. Tree acceptors and some of their applications. Journal of Comput. and Syst. Sci., 4:406451, 1970.

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J. E. Doner. Tree acceptors and some of their applications. Journal of Comput. and Syst. Sci., 4:406451, 1970.

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