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Training Tree Transducers
 IN HLTNAACL
, 2004
"... Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Treebased modeling still lacks many of the standard tools taken for granted in (finitestate) stringbased modeling. The theory of tree transducer automata provides a possible framework to ..."
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Cited by 113 (11 self)
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Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Treebased modeling still lacks many of the standard tools taken for granted in (finitestate) stringbased modeling. The theory of tree transducer automata provides a possible framework to draw on, as it has been worked out in an extensive literature. We motivate the use of tree transducers for natural language and address the training problem for probabilistic treetotree and treetostring transducers.
THE POWER OF EXTENDED TOPDOWN TREE TRANSDUCERS
"... Extended topdown tree transducers (transducteurs generalises descendants [Arnold, Dauchet: Bitransductions de forets. ICALP'76. Edinburgh University Press. 1976]) received renewed interest in the field of Natural Language Processing. Here those transducers are extensively and systematically s ..."
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Cited by 32 (23 self)
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Extended topdown tree transducers (transducteurs generalises descendants [Arnold, Dauchet: Bitransductions de forets. ICALP'76. Edinburgh University Press. 1976]) received renewed interest in the field of Natural Language Processing. Here those transducers are extensively and systematically studied. Their main properties are identified and their relation to classical topdown tree transducers is exactly characterized. The obtained properties completely explain the Hasse diagram of the induced classes of tree transformations. In addition, it is shown that most interesting classes of transformations computed by extended topdown tree transducers are not closed under composition.
Abstract Regular Tree Model Checking of Complex Dynamic Data Structures, 2006. Full version available on URL: http://www.fit.vutbr.cz/˜vojnar/pubs.php. ha l0 9, v er sio n  2 M ay
"... Abstract. We consider the verification of nonrecursive C programs manipulating dynamic linked data structures with possibly several next pointer selectors and with finite domain nonpointer data. We aim at checking basic memory consistency properties (no null pointer assignments, etc.) and shape ..."
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Cited by 26 (7 self)
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Abstract. We consider the verification of nonrecursive C programs manipulating dynamic linked data structures with possibly several next pointer selectors and with finite domain nonpointer data. We aim at checking basic memory consistency properties (no null pointer assignments, etc.) and shape invariants whose violation can be expressed in an existential fragment of a first order logic over graphs. We formalise this fragment as a logic for specifying bad memory patterns whose formulae may be translated to testers written in C that can be attached to the program, thus reducing the verification problem considered to checking reachability of an error control line. We encode configurations of programs, which are essentially shape graphs, in an original way as extended tree automata and we represent program statements by tree transducers. Then, we use the abstract regular tree model checking framework for a fully automated verification. The method has been implemented and successfully applied on several case studies. 1
The power of extended topdown tree transducers
 SIAM J. COMPUT
, 2008
"... Unfortunately, the class of transformations computed by linear extended topdown tree transducers with regular lookahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it ..."
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Cited by 17 (15 self)
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Unfortunately, the class of transformations computed by linear extended topdown tree transducers with regular lookahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it is demonstrated that every linear epsilonfree extended topdown tree transducer with regular lookahead can be implemented by a linear multi bottomup tree transducer. The class of transformations computed by the latter device is shown to be closed under composition, and to be included in the composition of the class of transformations computed by topdown tree transducers with itself. More precisely, it constitutes the composition closure of the class of transformations computed by nitecopying topdown tree transducers.
Decidability of the Finiteness of Ranges of Tree Transductions
 Inform. and Comput
, 1996
"... . The finiteness of ranges of tree transductions is shown to be decidable for TBY + , the composition closure of macro tree transductions. Furthermore, TBY + definable sets and TBY + computable relations are considered, which are obtained by viewing a tree as an expression that denotes an elem ..."
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Cited by 17 (7 self)
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. The finiteness of ranges of tree transductions is shown to be decidable for TBY + , the composition closure of macro tree transductions. Furthermore, TBY + definable sets and TBY + computable relations are considered, which are obtained by viewing a tree as an expression that denotes an element of a given algebra. A sufficient condition on the considered algebra is formulated under which the finiteness problem is decidable for TBY + definable sets and for the ranges of TBY + computable relations. The obtained result applies in particular to the class of string languages that can be defined by TBY + transductions via the yield mapping. This is a large class which is proved to form a substitutionclosed full AFL. 1 Introduction The finiteness problem is one of the classical decidability problems in formal language theory. For a given language of interest, one usually does not wish to know whether that language is finite (because it usually is not), but rather whether the l...
TREEBAG  A TreeBased Generator for Objects of Various Types
 Bericht Nr. 1/98, Universitat Bremen, Fachbereich Mathematik und Informatik
, 1998
"... . A software system called TreebagTreeBased Generatoris presented. The aim behind Treebag is to allow for the generation and visualization of objects of all kinds: pictures, trees, graphs, strings, numbers, etc. The basic principle is that tree generators like, for instance, regular tree gram ..."
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Cited by 9 (4 self)
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. A software system called TreebagTreeBased Generatoris presented. The aim behind Treebag is to allow for the generation and visualization of objects of all kinds: pictures, trees, graphs, strings, numbers, etc. The basic principle is that tree generators like, for instance, regular tree grammars, generate terms over symbols that are interpreted by appropriate algebras as operations on the domain of objects under consideration. Thus, every term is viewed as an expression that denotes one of the objects of interest. These objects can be visualized using appropriate displays. 1 Introduction In mathematics and computer science, one of the most natural and universal ways to denote elements of a given data space is to use expressions over a suitable set of operations, like p 3=7 + 5. The usefulness of this concept is even strengthened by the fact that such an expression may contain variablesin which case it does not denote a particular, single object, but a set of objects or a ...
Compositions of Tree Series Transformations
, 2005
"... Tree series transformations computed by bottomup and topdown tree series transducers are called bottomup and topdown tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottomup tree series transformations ..."
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Cited by 8 (6 self)
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Tree series transformations computed by bottomup and topdown tree series transducers are called bottomup and topdown tree series transformations, respectively. (Functional) compositions of such transformations are investigated. It turns out that the class of bottomup tree series transformations over a commutative and complete semiring is closed under leftcomposition with linear bottomup tree series transformations and rightcomposition with boolean deterministic bottomup tree series transformations. Moreover, it is shown that the class of topdown tree series transformations over a commutative and complete semiring is closed under rightcomposition with linear, nondeleting topdown tree series transformations. Finally, the composition of a boolean, deterministic, total topdown tree series transformation with a linear topdown tree series transformation is shown to be a topdown tree series transformation.
A Characterization of the Sets of Hypertrees Generated by HyperedgeReplacement Graph Grammars
 Theory of Computing Systems
, 1997
"... . A characterization of the sets of hypertrees generated by hyperedgereplacement graph grammars is given. The characterization says that these sets are exactly those which have the form val(T ), where T , a set of terms over hyperedgereplacement operations, is the output language of a finitecopying ..."
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Cited by 7 (2 self)
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. A characterization of the sets of hypertrees generated by hyperedgereplacement graph grammars is given. The characterization says that these sets are exactly those which have the form val(T ), where T , a set of terms over hyperedgereplacement operations, is the output language of a finitecopying topdown tree transducer. Furthermore, the terms in T may be required to consist of hyperedgereplacement operations whose underlying hypergraphs are hypertrees. The result is closely related to a similar characterization that was obtained for the case of string graphs by Engelfriet and Heyker some years ago. In fact, the results of this paper also yield a new proof for the characterization by Engelfriet and Heyker. 1 Introduction Hyperedgereplacement graph grammars, also called contextfree hypergraph grammars, are wellstudied devices for the generation of graph and hypergraph languages (see, e.g., [Hab92, Eng97, DHK97]). Their basic operation is the replacement of a nonterminal hypered...
TreeBased Generation of Languages of Fractals
 Theoretical Computer Science
, 1999
"... . The notion of Pinterpreted topdown tree generators is introduced, combining the nondeterministic nature of grammars as known from formal language theory with the innite renement of pictures studied in fractal geometry. 1 Introduction This paper introduces an approach to generate languages of ..."
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Cited by 5 (4 self)
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. The notion of Pinterpreted topdown tree generators is introduced, combining the nondeterministic nature of grammars as known from formal language theory with the innite renement of pictures studied in fractal geometry. 1 Introduction This paper introduces an approach to generate languages of fractals, thus combining fractal geometry with one of the main ideas of formal language theory, namely to consider innite sets of objects related by a common grammatical description. The theory of formal languages is normally concerned with the grammatical generation of sets of discrete objects, these sets being called languages. Traditional questions ask for the properties of these languages and their recognition by various sorts of automata. While the objects of interest had initially been words, the ideas were soon taken up by researchers interested in more complex data structures like arrays, trees, and graphs (see the recently published books [RS97] for a representative overview of...
Categorical Views on Computations on Trees (Extended Abstract)
"... Abstract. Computations on trees form a classical topic in computing. These computations can be described in terms of machines (typically called tree transducers), or in terms of functions. This paper focuses on three flavors of bottomup computations, of increasing generality. It brings categorical ..."
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Cited by 4 (0 self)
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Abstract. Computations on trees form a classical topic in computing. These computations can be described in terms of machines (typically called tree transducers), or in terms of functions. This paper focuses on three flavors of bottomup computations, of increasing generality. It brings categorical clarity by identifying a category of tree transducers together with two different behavior functors. The first sends a tree transducer to a coKleisli or biKleisli map (describing the contribution of each local node in an input tree to the global transformation) and the second to a tree function (the global tree transformation). The first behavior functor has an adjoint realization functor, like in Goguen’s early work on automata. Further categorical structure, in the form of Hughes’s Arrows, appears in properly parameterized versions of these structures. 1