Joost Engelfriet. Top-down tree transducer with regular look-ahead. Mathematical Systems Theory, 9(3):289--303, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and protocols based on such receive send actions non looping. In this paper, a protocol model is proposed in which receive send actions are described by (non deterministic) tree transducers with regular look ahead (TTLAs) Roughly speaking, such automata, which were rst introduced by Engelfriet [10], are given by a set of rewrite rules of a certain kind, and they transform input messages to output messages by iteratively applying the rewrite rules to the input message. Thus, in contrast to models for non looping protocols, in our model we can describe what we will call iterative protocols, ....

....Tree transducers [12] perform transformations on terms. They obtain a term as input and return (another) term as output. Non deterministic tree transducers may produce di erent output terms on one input term. Here, we consider (non deterministic) topdown tree transducers with regular look ahead [10], which work as follows: They read the head symbol f of the input term f(t 0 ; t n 1 ) depending on the current state replace it by some term, and then proceed to transform the subterms t i in the same fashion. Before the transformation takes place, the transducer may check whether the ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289-303, 1976.

....[Bak78] for example) which translate trees into strings. But crucial role of tree structure have increased later. Many generalizations have been introduced, for example generalized nite state transformations which generalize both the top down and the bottom up tree transducers (J. Engelfriet [Eng77] modular tree transducers (H. Vogler [EV91] synchronized tree automata (K. Salomaa [Sal94] alternating tree automata (G.Slutzki [Slu85] deterministic top down tree transducers with iterated look ahead (G. Slutzki, S. Vgvlgyi [SV95] Ground tree transducers GTT are studied in Chapter 3 of ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

....a generalization of rational transformations in the word case (see [1] 3] for a synthesis) were introduced by W.C. Rounds [15] and J.W. Thatcher [17] They have been widely studied. The authors have chosen either the algebraic point of view ( 2] 9] 4] or the machine point of view ( 7] [8], 16] Naturally, the question arises whether or not the results obtained for transformations in the word case can be transferred to tree transducers. The situation is different. For instance, we have to distinguish two main classes of tree transducers: top down transducers which process the ....

....are first studied (section 4.3) The results we obtain are valid in the general case (section 4.4) Finally, we extend the previous result to bottom up transducers (section 4.5) 2 Preliminaries Main definitions and results about tree transducers can be found in J. Engelfriet s papers ( 7] [8], 10] and in the book of F.Gecseg and M.Steinby [13] In this section, we just give basic definitions and properties used in the paper. 2.1 Trees A ranked alphabet is a pair ( Sigma; ae) where Sigma is a finite alphabet and ae is a mapping from Sigma to IN. Usually, we will write Sigma for ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory. Vol 10. pp 289-303. 1977.

....this class of transducers. 1 Introduction Tree transducers, which are a generalization of rational transformations in the word case (see [1] 4] for a synthesis) have been widely studied. The authors have choosed either the algebraic point of view ( 2] 5] or the machine point of view ( 7] [8], 11] for instance) In the word case, the main results of decidability of equivalence are: Equivalence is undecidable in the non deterministic case (T.Griffiths 1968) Equivalence is decidable in the deterministic one (Bird 1973, Valiant 1974) The same results have been obtained in trees. ....

....denotes the depth of t. ffl For all p 2 IN, p] denotes the set f1; pg. A torsion from [p] to [q] is a mapping from [p] to [q] We denote it by q; 1) p) 2.2 Letter to Letter Top down Tree Transducers Main definitions and results can be found in J. Engelfriet s papers ( 7] [8]) and in the book of F.Gecseg and M.Steinby [10] We just give the definitions and properties used in this paper. Definitions. A top down tree transducer is a 5 tuple T = Sigma ; Delta; Q; I; R where Sigma and Delta are the ranked alphabets of respectively input and output symbols, Q is ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory. Vol 10. pp 289-303. 1977.

.... Theta T Delta computed by M can be defined (where T Sigma and T Delta are the sets of input trees and output trees, respectively) Since the seventies, tree transducers have been studied intensively. The first substantial papers dealt with (de )composition and hierarchy results [Bak79, Eng75, Eng77, Eng82] In [FV92] a method of deciding the equivalence of the compositions of classes of tree transformations is overviewed. Survey articles and books are [GS84, GS97, CDG 97, FV98] Recently, a characterization of tree transformation classes in terms of monadic second order logic has been ....

J. Engelfriet. Top--down tree transducers with regular look--ahead. Math. Systems Theory, 10:289--303, 1977.

....tree SigmaX language can be generated a tree transducer, different kinds of transformations can be implemented using different tree homomorphisms. To increase the transformational capability, more powerful transducers are introduced as well. A descending tree transducer with regular look ahead [Eng77b] allows to inspect 24 the subtrees of a node before processing it, however, restricting extracted information to be finite and regular. The rules in macro tree transducers [EV85] are in the form q(oe( 1 ; m ) y 1 ; y m ) t where the first parameter defines the syntax for a ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289--303, 1977.

....move up in the document and will always terminate. We denote this fragment by DTL mso d . We define a computational model for DTL mso d : the top down tree transducer with look ahead. This is a finite state device obtained as the natural generalization of the usual top down tree transducer [24, 9] over ranked trees. The basic idea of going from ranked to unranked trees is the one of Bruggemann Klein, Murata and Wood [4] replace recursive calls by regular (string) languages of recursive calls. We show that these transducers correspond exactly to DTL mso d programs. As in the ranked case ....

....labels from left to right is a non context free string language (for p i = b i it is fww j w 2 fb 1 ; b n g g) We show, however, that the output of a DTL mso d program can always be restricted to a (generalized) DTD. Similar results are known for ranked top down tree transducers [24, 9]. It follows from Theorem 16 and results of Fulop [14] that it is even undecidable whether the output schema of a DTL mso d (or even a DTL reg ) program can be described by a (generalized) DTD. We now exhibit some relevant optimization problems that are decidable: it is decidable whether the ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Math. Systems Theory, 10:289--303, 1977.

....is a linear nondeleting top down tree transduction. Pi We call a linear nondeleting top down tree transducer td 00 the composition of td and td 0 if it computes the composed transduction td 0 ffi td . Next, we recall the definition of top down tree transducers with regular look ahead [Eng77]. For this, it is necessary to say what a regular set of terms is. One of the known characterizations (that is used as a definition here) is in terms of top down tree transducers into the boolean algebra B (see Courcelle [Cou90] Proposition 1.5 (i) and (iv) and Drewes [Dre94] Theorem 5.1) Here ....

....of a rule with left hand side fl(f(x 1 ; x n ) is restricted to those subterms fl(f(t 1 ; t n ) where t 1 ; t n belong to certain regular sets of terms given in the definition of the transducer. 3. 9 Definition (top down tree transducer with regular look ahead, cf. [Eng77, GS84]) Let Sigma; Sigma 0 be signatures and let Gamma be a set of states disjoint with Sigma [ Sigma 0 . A top down tree transducer td R : T( Sigma) T( Sigma 0 ) with regular look ahead is a tuple td R = Sigma; Sigma 0 ; Gamma; R; Gamma 0 ) such that ffl R is a set of pairs ....

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory 10, 289--303, 1977.

....or subtree, thus realizing the transformation in an effective, inductive, way. twelf Tree automata and tree grammars 3. 1 Recognizable tree languages The definitions of tree automata and tree grammars used in this thesis are from [Eng74] Nearly the same definitions are used in [Eng75] and [Eng77]. Another well known source for the theory of tree automata and tree grammars is [GecSte84] 3.1.1 Finite tree automata and regular tree grammars A finite tree automaton is very much like a finite state automaton for the string case. When the automaton is in a certain state, it can recognize one ....

....closure and decidability results about bottom up finite tree transformations and top down finite tree transformations. Only the results that are needed in the remainder of this thesis are presented here. Many more, and the proofs of the ones presented here, can be found in [Eng74] Eng75] and [Eng77]. twentyfour Tree automata and tree grammars Theorem 3.59 RECOG is closed under inverse bottom up and top down tree transformations (in particular under inverse homomorphisms) Proof In [Eng74, page 112] Definition 3.60 Let K be a class of tree transformations. A K surface tree language is a ....

Joost Engelfriet, Top-down Tree Transducers with Regular Look-ahead , Mathematical Systems Theory, Vol. 10, 1977, pp. 289--303.

....machine computes a transformation of strings. The study of top down tree transducers was begun in the seventies by Rounds and Thatcher [Rou70, Tha70, Tha73] and was continued by several other authors. In this paper, we will mainly consider the variant defined and investigated by Engelfriet in [Eng77] (see also [Eng78, ERS80, FV89, SV95, GV96] called top down tree transducer with regular look ahead. For surveys on the theory of tree languages and tree transductions see [GS84, NP92, GS97] Throughout the paper N denotes the set of natural numbers (including 0) and N = N nf0g. For n 2 N , ....

....of interest for this paper are computed by finite state devices called top down tree transducers, because they compute tree transductions by processing an input tree (i.e. a term viewed as a tree) from the top down. 2. 2 Definition (top down tree transducer with regular look ahead, cf. [Eng77]) A top down tree transducer with regular look ahead (tdr transducer) is a system tdr = Sigma; Sigma 0 ; Gamma; R; fl 0 ) where Sigma and Sigma 0 are finite signatures of input and output symbols, respectively, Gamma with Gamma ( Sigma [ Sigma 0 ) is a finite signature of ....

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Joost Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289--303, 1977.

....set of terms generated by g is L(g) ft 2 T Sigma j S P tg, where P denotes the term rewrite relation determined by P and P its reflexive and transitive closure. The set L(g) is called a regular set of terms. A top down tree transducer with regular look ahead (tdr transducer, see [Eng77]) is a system tdr = Sigma ; Sigma 0 ; Gamma; R; fl 0 ) where Sigma and Sigma 0 are finite signatures of input and output symbols, respectively, Gamma with Gamma ( Sigma [ Sigma 0 ) is a finite signature of states each of which has rank 1, fl 0 2 Gamma is the initial state, ....

Joost Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289--303, 1977.

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Joost Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289-303, 1977.

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Joost Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289-303, 1977.

....ends the proof of Claim 2. It was mentioned in the Conclusions of [EV85] as an open problem whether the class of macro tree translations is closed under composition with T R , the class of top down tree translations with regular look ahead. Since T R equals D t QRELABT (see Theorem 2. 6 of [Eng77]) it follows from Lemma 11 that MTT T R MTT D t QRELAB T MTT T , and by Lemma 5, MTT T MTT . Corollary 12. MTT T R MTT. We now move to the second closure property. The main part of the proof of this closure property consists of proving Theorem 15 which says that, for a class ....

J. Engelfriet. Top-down tree transducers with regular look-ahead. Math. Systems Theory, 10:289-303, 1977.

....attribute grammar which just preprocesses the input tree by relabeling its nodes: all attributes have nitely many values and one of the attributes holds the new label of each node. This is the look ahead part of the att R ; the R stands for relabeling or for regular look ahead (cf. [Eng1]) where regular is used to refer to nite state devices (in this case an attribute grammar of which all attributes have nitely many values) The second attribute grammar is an attributed tree transducer (introduced in [F ul] see also [EngFil] which performs the actual computation: the values ....

....we consider total deterministic transducers only. We consider three types of such transducers. First the top down tree transducer, which is well known to be equivalent with the os attributed tree transducer (see [CouFra,F ul] The top down tree transducer was extended with regular look ahead in [Eng1]. Let T R denote the class of all tree transductions that are computed by top down tree transducers with regular look ahead. It is not dicult to understand, and is proved in Theorem 4.4 of [EngMan] that preprocessing the input tree with an attributed relabeling has the same e ect as regular ....

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J. Engelfriet; Top-down tree transducers with regular look-ahead, Math. Systems Theory 10 (1977), 289-303

....S Delta can easily be obtained from the tree transducer in the proof of Lemma 17) Obviously R Sigma = Gamma1 (S Delta ) ft 2 T Sigma j type(val(t) g. Since the class of regular tree languages is closed under inverse bottom up and top down tree transductions (see Lemma 1. 2 of [22]) and under intersection, R Sigma is regular. If) To show that f is F transducible, let Sigma be a finite subset of F. Consider a total deterministic bottom up tree automaton A that recognizes R Sigma , and let Q fin be its set of final states. Construct the total deterministic bottomup ....

J.Engelfriet; Top-down tree transducers with regular look-ahead, Math. Syst. Theory 10 (1977), 289-303

....6 The class of all translations which can be realized by macro tree transducers is denoted by MTT. The classes of translations realized by top down tree transducers and by top down relabelings are denoted by T and T REL, respectively. Let us now add regular look ahead to a macro tree transducer [EV85, Eng77]. Definition 3.3 (MTT with regular look ahead) A macro tree transducer with regular look ahead (for short, MTT R ) is a tuple M = Q; P; Sigma; Delta; q 0 ; R; h) where (P; Sigma; h) is a finite state tree automaton, called the look ahead automaton of M, the components Q, Sigma, Delta, ....

.... Theta V j i; j 2 N; hc; ii occurs in rhs(hc 0 ; ji; s[u] g. 2 Attributed Relabelings A translation from trees to trees is called a relabeling, if for (s; t) 2 , t is obtained from s by merely changing the labels of the nodes of s. The classes DBQREL and DTQREL of finite state relabelings of [Eng77, Eng75], which are based on bottom up and top down tree transducers, respectively, are well known classes of (partial) relabelings. The class T REL of top down relabelings (Definition 3.1) is, in fact, the class of total relabelings in DTQREL, and T R REL is its obvious extension with regular ....

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Math. Systems Theory, 10:289--303, 1977.

....R r ) into (R 0 ; oe; R 0 r ) where R 0 = R Sigma 1 (with the exception that R 0 = fg when oe = and similarly for R 0 r . We observe here that this notion of regular look around generalizes the well known notion of regular look ahead for one way automata (see, e.g. [Nij82, Eng77]) Mso instructions. For a 2gsm with mso instructions (2gsm mso) the test and the moves of each instruction are given by mso formulas. To be precise, for (p; t; q 1 ; ff 1 ; 1 ; q 0 ; ff 0 ; 0 ) 2 ffi, t is given as a formula (x) in MSO( Sigma 1 [ f ; ag; with one free node variable x, and ....

J. Engelfriet, Top-down tree transducers with regular look-ahead, Mathematical Systems Theory 10 (1977) 289--303. cited: 12 58

....Those investigated in this paper are composed of three basic types of tree transductions. On the one hand, there are the top down and bottom up tree transductions, whose investigation began in the seventies by Rounds and Thatcher [Rou70a, Tha70a, Tha70b, Tha73] and was continued in, e.g. [Eng75a, Eng77, Bak78b, Bak78a, Bak79, Eng82, FV89, AD94, Sei94a, SV95, DF96, GV96]. These tree transductions are defined by the use of restricted rewrite rules, processing a tree from the top down or from the bottom up, respectively. The third one of the basic types of tree transductions considered acts on input trees over a signature that consists of symbols from an underlying ....

....one (see [Eng82] collapses into lTD ffi dRELAB in this case. This is stated as a lemma below. 3. 5 Lemma There is an algorithm that takes as input a tree transduction T Sigma Theta T Sigma 0 3 These are the classes denoted by QRELAB and DQRELAB in [Eng75a] and by QREL and DBQREL in [Eng77]. in TB such that Sigma 0 is monadic, and constructs a linear top down tree transducer td and a deterministic relabelling rel such that td ffi rel = Proof. This follows from known results about the classes TDR = TD ffi dRELAB and lTDR = lTD ffi dRELAB of top down tree transductions ....

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Joost Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289--303, 1977.

....only. We consider three types of such transducers. First the top down tree transducer, which is well known to be equivalent with the os attributed tree transducer (see [CouFra, Ful] To ensure closure under composition, the top down tree transducer was extended with regular look ahead in [Eng1]. Let T R denote the class of all tree transductions that are computed by top down tree transducers with regular look ahead. It is not difficult to understand, and is proved in [EngMan] that preprocessing the input tree with an attributed relabeling has the same effect as regular look ahead. ....

....effect as regular look ahead. This implies that att rel ffi att os = T R . Thus, by Theorem 18, mso tgt dir = T R , i.e. the direction preserving mso definable term transductions are exactly the top down tree transductions with regular look ahead. Since T R is closed under composition (see [Eng1]) this implies that mso tgt dir is closed under composition (see Proposition 2 and the discussion following it) Second the bottom up tree transducer, which is incomparable with the topdown tree transducer. The result of [FulVag] shows that not every bottom up tree transducer can be simulated by ....

J. Engelfriet; Top-down tree transducers with regular look-ahead, Math. Systems Theory 10 (1977), 289--303

....(for short: td t transducers) respectively, in the sense that they operate in exactly the same way, but the output objects are special graphs (viz. hypergraphs) rather than trees. Before further discussing bu tg transducers, td tg transducers, and our comparison, we would like to recall from [Eng75, Eng77] the comparison of td t transducers and bu t transducers, because, at first sight surprisingly, that comparison yields a different result: it has been shown in [Eng77] that the classes tT and tB of tree to tree translations which are computed by td t transducers and bu t transducers, respectively, ....

....than trees. Before further discussing bu tg transducers, td tg transducers, and our comparison, we would like to recall from [Eng75, Eng77] the comparison of td t transducers and bu t transducers, because, at first sight surprisingly, that comparison yields a different result: it has been shown in [Eng77] that the classes tT and tB of tree to tree translations which are computed by td t transducers and bu t transducers, respectively, are incomparable. Thus, we will first have a look at the reasons for this incomparability (cf. Section 3 of [Eng77] second we will discuss the concept of bu tg ....

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Math. Systems Theory, 10:289--303, 1977.

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Joost Engelfriet. Top-down tree transducer with regular look-ahead. Mathematical Systems Theory, 9(3):289--303, 1977.

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

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J. Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical System Theory, 10:198231, 1977.

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J. Engelfriet. Top-down Tree Transducers with Regular Look-ahead. Mathematical system theory. Vol 10. pp 289-303. 1977.

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Joost Engelfriet. Top-down tree transducers with regular look-ahead. Mathematical Systems Theory, 10:289-303, 1977.

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