R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Journal of Computer and System Sciences, 61(1):1--50, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....reader to [42] for a more detailed overview of pattern languages based on tree automata. 5 Tree walking automata Next, we focus on computation by tree walking. This is a well known paradigm from formal language theory studied in the context of attribute grammars and tree transformations [4, 7, 16]. This paradigm materialized in XML research in various ways. Indeed, a first instance of tree walking is provided by the caterpillar expressions of Bruggemann Klein and Wood [9] Further, Milo, Suciu, and Vianu [34] defined a tree walking tree transducer model with pebbles as an abstract model ....

R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Journal of Computer and System Sciences, 61(1):1--50, 2000.

....of the right hand side of a production, respectively. By designating odd as the result attribute, on an input tree the BAG retrieves all nodes for which odd is true. Although BAGs constitute a seemingly simple formalism, it can be shown that BAGs express precisely all MSO definable unary patterns [27, 3]. XML documents, however, are usually described by extended context free grammars (DTDs) These are grammars with regular expressions on the righthand sides of productions. The above context free grammar could be specified, for instance, like List # L # , L # p. One problem that arises when ....

R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Journal of Computer and System Sciences, 61(1):1--50, 2000.

....If rub 0;1 (L) 2 yMTT (L) then for every n 2, rub b1 ; b n (L) 2 yMTT (L) Proof. It is straightforward to construct an MTT M yield which translates every input tree into its yield, represented as a monadic tree (e.g. oe(a; b) is translated into a( b) In fact in Example 1(6, yield) of [BE98] it is shown that this tree translation can be defined in monadic second order logic (MSO) By Theorem 7.1 of [EM98] the MSO definable tree translations are precisely those realized by finite copying macro tree transducers. We will now define a top down tree transducer Mn which translates a ....

....K over Delta with yK = rub 0;1 (L) yMn ( M yield (K) rub b1 ; b n (L) We can now compose M yield with Mn to obtain again a finite copying MTT which realizes M yield ffi Mn . This follows from the fact that MSO definable translations are closed under composition (cf. Proposition 2 of [BE98]) and that Mn is finite copying (it is even linear, i.e. 1 copying) In Corollary 7.9 of [EM98] it is shown that finite copying MTTs with regular look ahead have the same string generating power as finite copying top down tree transducers with regular look ahead. Hence, there is a finite copying ....

R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Technical Report 98-02, Leiden University, 1998.

....Transformations Zolt an Fulop Heiko Vogler Department of Computer Science Department of Computer Science University of Szeged Technical University of Dresden Arp ad t er 2. H 6720 Szeged, Hungary D 01062 Dresden, Germany E mail: fulop inf.u szeged.hu E mail: vogler inf.tu dresden.de October 23, 2000 Abstract: We generalize bottom up tree transducers and top down tree transducers to the concept of bottom up tree series transducer and top down tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from ....

....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 proved [BE00, EM99] Now let us briefly review the second origin of tree series transducers: automata with multiplicities. Let M = Q; Sigma; q 0 ; Q d ) be a usual finite state string automaton where Q is the set of states, Sigma the set of input symbols, Q Theta Sigma P(Q) the transition ....

R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Journal of Computer and System Sciences, 61:1--50, 2000. 22

....and context free tree grammars (see, e.g. EV85, CF82, FV98] Their (tree to tree) transductions form a large class, containing the translations of attribute grammars. More recently, tree transductions that can be specified in monadic second order (MSO) logic have been considered (see, e.g. [Cou94, BE98, EM99, KS94]) It is shown in [BE98] that these MSO definable tree transductions can be computed by (a special type of) attribute grammars. Thus, as stated in [EM99] every MSO definable tree transduction can be realized by an MTT. However, not every macro tree transduction is MSO definable. We have ....

....[EV85, CF82, FV98] Their (tree to tree) transductions form a large class, containing the translations of attribute grammars. More recently, tree transductions that can be specified in monadic second order (MSO) logic have been considered (see, e.g. Cou94, BE98, EM99, KS94] It is shown in [BE98] that these MSO definable tree transductions can be computed by (a special type of) attribute grammars. Thus, as stated in [EM99] every MSO definable tree transduction can be realized by an MTT. However, not every macro tree transduction is MSO definable. We have considered the question, which ....

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R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Technical Report 98-02, Leiden University, 1998. To appear in J. of Comp. Syst. Sci.

....transductions to regular tree languages [EvO97, CE95] If, for an MSO transduction, we restrict the input and output graphs to be (node labeled, ordered) trees, then we obtain a function from trees to trees, i.e. a tree translation. In This work was supported by the EC TMR Network GETGRATS. 1 [BE98] the class of MSO definable tree translations was investigated and it was proved that it equals the class of tree translations realized by attributed tree transducers (ATTs) with look ahead which are single use restricted (sur) ATTs are a variation of attribute grammars in which all attribute ....

....use restriction for ATTs can be generalized to MTTs and it can be shown that, in the presence of look ahead, the classes of translations realized by single use restricted MTTs and ATTs are equal. This is our first main result. Given a tree translation defined in MSO we can, via the result of [BE98], construct an MTT with regular look ahead which is single use restricted and which realizes . Conversely, given a single use restricted MTT with regular look ahead we can construct a corresponding MSO transducer. However, the single use restriction is a rather strong restriction on the rules of ....

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R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Technical Report 9802, Leiden University, January 1998. (to appear in J. of Comp. Syst. Sci.) http://www.wi.leidenuniv.nl/TechRep/1998/tr98-02.html.

.... systems, model checking, see the monograph [Kur94] Generalizations of the result of Buchi and Elgot include infinite strings [Buc62] trees [Don70, ThWr68] traces (a syntactic model for concurrency) Ebi95] texts (strings with an additional ordering) HoPa97] and tree to tree transductions [BlEn97, EnMa98]. We refer to [Tho97] for an overview of the study of formal languages within the framework of mathematical logic. We give a short description of the two formalisms of regular string transductions that we study in this paper. We mainly consider the deterministic case. A two way finite state ....

R. Bloem, J. Engelfriet, A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Leiden University Technical Report, 97-03, August 1997. http://www.wi.leidenuniv.nl/TechRep/1997/tr97-03.html cited: 2

....and context free tree grammars (see, e.g. EV85, CF82, FV98] Their (tree to tree) transductions form a large class, containing the translations of attribute grammars. More recently, tree transductions that can be specified in monadic second order (MSO) logic have been considered (see, e.g. [Cou94, BE98, EM98, KS94]) It is shown in [BE98] that these MSO definable tree transductions can be computed by (a special type of) attribute grammars. Thus, as stated in [EM98] every MSO definable tree transduction can be realized by an MTT. However, not every macro tree transduction is MSO definable. We have ....

....[EV85, CF82, FV98] Their (tree to tree) transductions form a large class, containing the translations of attribute grammars. More recently, tree transductions that can be specified in monadic second order (MSO) logic have been considered (see, e.g. Cou94, BE98, EM98, KS94] It is shown in [BE98] that these MSO definable tree transductions can be computed by (a special type of) attribute grammars. Thus, as stated in [EM98] every MSO definable tree transduction can be realized by an MTT. However, not every macro tree transduction is MSO definable. We have considered the question, which ....

[Article contains additional citation context not shown here]

R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Technical Report 98-02, Leiden University, 1998. To appear in J. of Comp. Syst. Sci.

....are trees: mso tree transductions. Since the edges of the output tree can be viewed as pointers (to the i th child, for each i) they correspond to functions on the nodes of the input tree, as explained above. Thus, they can be computed by deterministic tree walking automata. This is used in [Blo, BloEng2] to show that the mso tree transductions can be computed by two stage attribute grammars: in the first stage the mso tests on the nodes of the input tree are evaluated, by attributes of type boolean, and in the second stage the output tree is computed, by attributes of type tree. After recalling ....

....if all outgoing edges of each node of the output graph have distinct labels (as, e.g. for term graphs) then, by Theorem 21, it can be computed in linear time. In particular, mso definable tree transductions can be computed in linear time. As mentioned in the Introduction, it is shown in [Blo, BloEng2] that they can in fact be computed by two stage attribute grammars. ....

R. Bloem, J. Engelfriet; A comparison of tree transductions defined by monadic second order logic and by attribute grammars, in preparation

....(cf. Cou94] taking regular tree languages as input. This means that TR(HR) TR(MSOT (REGT ) Hence the particular MSO transductions involved translate trees into trees; moreover, they can be restricted to total functions. Let us denote this class of tree to tree transductions by MSOTT. In [BE98] MSOTT is characterized in terms of attribute grammars. We now present a characterization of this class in terms of MTTs (which are more powerful than attribute grammars) proved in [EM98] As it turns out, the feature of regular look ahead (cf. EV85] must be added to the MTTs in order to obtain ....

R. Bloem, J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Technical Report 98-02, Leiden University, 1998.

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R. Bloem and J. Engelfriet. A comparison of tree transductions defined by monadic second order logic and by attribute grammars. Journal of Computer and System Sciences, 61(1):1--50, 2000.

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