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55
Macro Tree Transducers, Attribute Grammars, and MSO Definable Tree Translations
 Inform. and Comput
, 1998
"... A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with reg ..."
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Cited by 46 (20 self)
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A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs) with regular lookahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular lookahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular lookahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the ...
Structured document transformations based on XSL
 In DBPL
, 1999
"... Abstract. Based on the recursion mechanism of the XML transformation language XSL, the document transformation language DTL is defined. First the instantiation DTL reg is considered that uses regular expressions as pattern language. This instantiation closely resembles the navigation mechanism of XS ..."
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Cited by 38 (12 self)
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Abstract. Based on the recursion mechanism of the XML transformation language XSL, the document transformation language DTL is defined. First the instantiation DTL reg is considered that uses regular expressions as pattern language. This instantiation closely resembles the navigation mechanism of XSL. For DTL reg the complexity of relevant decision problems such as termination of programs, usefulness of rules and equivalence of selection patterns, is addressed. Next, a much more powerful abstraction of XSL is considered that uses monadic secondorder logic formulas as pattern language (DTL mso). If DTL mso is restricted to topdown transformations (DTL mso d), then a computational model can be defined which is a natural generalization to unranked trees of topdown tree transducers with lookahead. The lookahead can be realized by a straightforward bottomup preprocessing pass through the document. The size of the output of an XSL program is at most exponential in the size of the input. By restricting copying in XSL a decidable fragment of DTL mso d programs is obtained which induces transformations of linear size increase (safe DTL mso d). It is shown that the emptiness and finiteness problems are decidable for ranges of DTL mso d programs and that the ranges are closed under intersection with generalized Document Type Definitions (DTDs). 1
Bottomup and Topdown Tree Series Transformations
 J. Autom. Lang. Combin
, 2000
"... We generalize bottomup tree transducers and topdown tree transducers to the concept of bottomup tree series transducer and topdown tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some s ..."
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Cited by 37 (6 self)
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We generalize bottomup tree transducers and topdown tree transducers to the concept of bottomup tree series transducer and topdown tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some semiring. We associate two semantics with a tree series transducer: a mapping which transforms trees into tree series (for short: tree to tree series transformation or tts transformation), and a mapping which transforms tree series into tree series (for short: tree series transformation or tsts transformation). We show that the standard case of tree transducers is reobtained by choosing the boolean semiring under the tts semantics. Also, for each of the two types of tree series transducers and for both types of semantics, we prove a characterization which generalizes in a straightforward way the corresponding characterization result for the underlying tree transducer class. Mo...
Extrapolating Tree Transformations
, 2002
"... We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R # (L) where R i ..."
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Cited by 25 (6 self)
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We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R # (L) where R is a regular tree transducer and L is a regular tree language. The construction
Composition of functions with accumulating parameters
 Journal of Functional Programming
, 2004
"... Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such function ..."
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Cited by 20 (9 self)
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Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such functions, where classical deforestation techniques fail. In order to do so, given two macro tree transducers under appropriate restrictions, we construct a single macro tree transducer that implements the composition of the two original ones. The imposed restrictions are more liberal than those in the literature on macro tree transducer composition, thus generalising previous results.
A Kleene theorem for weighted tree automata
 Theory of Computing Systems
, 2002
"... In this paper we prove Kleene's result for tree series over a commutative and idempotent semiring A (which is not necessarily complete or continuous), i.e., the class of recognizable tree series over A and the class of rational tree series over A are equal. We show the result by direct automatatheo ..."
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Cited by 17 (8 self)
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In this paper we prove Kleene's result for tree series over a commutative and idempotent semiring A (which is not necessarily complete or continuous), i.e., the class of recognizable tree series over A and the class of rational tree series over A are equal. We show the result by direct automatatheoretic constructions and prove their correctness.
Transformation of Structured Documents
, 1995
"... Structure definitions of documents have been used successfully for inputting and formatting in text processing systems. This report considers transformations between different representations of structured documents and studies possibilities to extend the use of structure definitions to document tra ..."
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Cited by 12 (4 self)
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Structure definitions of documents have been used successfully for inputting and formatting in text processing systems. This report considers transformations between different representations of structured documents and studies possibilities to extend the use of structure definitions to document transformations and to discover algorithmic methods for carrying out transformations. Documents are presented as parse trees for contextfree grammars and transformations are made from parse tree to parse tree. First, the report describes differences of manuscript styles required by various scientific journals and presents a declarative classification for structure differences between two parse trees. Second, a set of tree transformation methods are described and their suitability for transformations between documents having a structure difference in each defined class is analyzed. For each class several methods may or must be used and only certain kinds of differences can be managed automatica...
The Complexity of Compositions of Deterministic Tree Transducers
 Proceedings of the 22nd Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2002), volume 2556 of LNCS
, 2002
"... Macro tree transducers can simulate most models of tree transducers (e.g., topdown and bottomup tree transducers, attribute grammars, and pebble tree transducers which, in turn, can simulate all known models of XML transformers). The string languages generated by compositions of macro tree transdu ..."
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Cited by 11 (6 self)
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Macro tree transducers can simulate most models of tree transducers (e.g., topdown and bottomup tree transducers, attribute grammars, and pebble tree transducers which, in turn, can simulate all known models of XML transformers). The string languages generated by compositions of macro tree transducers (obtained by reading the leaves of the output trees) form a large class which contains, e.g., the IO hierarchy and the EDT0L control hierarchy. Consider an arbitrary composition of (deterministic) macro tree transducers. How dicffiult is it, for a given input tree s, to compute the translation t = (s)? It is shown that this problem can be solved (on a RAM) in time linear in the sum of the sizes of s and t. Moreover, the problem to determine, for a given t of size n, whether or not there is an input tree s such that t = (s) is in DSPACE(n); this means that output languages of compositions of macro tree transducers are deterministic contextsensitive. The involved technique of compressing intermediate results of the composition, also gives a new proof of the fact that the finiteness problem for 's range is decidable.
Extended Multi BottomUp Tree Transducers
"... Abstract. Extended multi bottomup tree transducers are de ned and investigated. They are an extension of multi bottomup tree transducers by arbitrary, not just shallow, lefthand sides of rules; this includes rules that do not consume input. It is shown that such transducers can compute any transf ..."
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Cited by 9 (5 self)
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Abstract. Extended multi bottomup tree transducers are de ned and investigated. They are an extension of multi bottomup tree transducers by arbitrary, not just shallow, lefthand sides of rules; this includes rules that do not consume input. It is shown that such transducers can compute any transformation that is computed by a linear extended topdown tree transducer. Moreover, the classical composition results for bottomup tree transducers are generalized to extended multi bottomup tree transducers. Finally, a characterization in terms of extended topdown tree transducers is presented. 1