Results 11 
17 of
17
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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
Compositions of bottomup tree series transformations
 UNIVERSITY OF SZEGED
, 2005
"... Tree series transformations computed by bottomup tree series transducers are called bottomup tree series transformations. (Functional) compositions of such transformations are investigated. It turns out that bottomup tree series transformations over commutative and ...complete semirings are clos ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Tree series transformations computed by bottomup tree series transducers are called bottomup tree series transformations. (Functional) compositions of such transformations are investigated. It turns out that bottomup tree series transformations over commutative and ...complete semirings are closed under leftcomposition with linear bottomup tree series transformations and rightcomposition with boolean deterministic bottomup tree series transformations.
Hierarchies of Tree Series Transformations Revisited
, 2006
"... Tree series transformations computed by polynomial topdown and bottomup tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutativ ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Tree series transformations computed by polynomial topdown and bottomup tree series transducers are considered. The hierarchy of tree series transformations obtained in [Fülöp, Gazdag, Vogler: Hierarchies of Tree Series Transformations. Theoret. Comput. Sci. 314(3), p. 387–429, 2004] for commutative izzsemirings (izz abbreviates idempotent, zerosum and zerodivisor free) is generalized to arbitrary positive (i. e., zerosum and zerodivisor free) commutative semirings. The latter class of semirings includes prominent examples such as the natural numbers semiring and the least common multiple semiring, which are not members of the former class.
Compositions of Topdown Tree Transducers with "rules
"... Abstract. Topdown tree transducers with "rules ("tdtt) are a restricted version of extended topdown tree transducers. They are implemented in the framework Tiburon and ful ll some criteria desirable in a machine translation model. However, they compute a class of transformations that is not close ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. Topdown tree transducers with "rules ("tdtt) are a restricted version of extended topdown tree transducers. They are implemented in the framework Tiburon and ful ll some criteria desirable in a machine translation model. However, they compute a class of transformations that is not closed under composition (not even for linear and nondeleting "tdtt). A composition construction that composes "tdtt M and N is presented. It is correct whenever (i) M has at most one output symbol in each rule, (ii) M is deterministic or N is linear, and (iii) M is total or N is nondeleting. This corresponds nicely to a classical composition result by Baker. 1
TreeSeriestoTreeSeries Transformations
"... Abstract. We investigate the treeseriestotreeseries (tsts) transformation computed by tree series transducers. Unless the used semiring is complete, this transformation is, in general, not wellde ned. In practice, many used semirings are not complete (like the probability semiring). We establi ..."
Abstract
 Add to MetaCart
Abstract. We investigate the treeseriestotreeseries (tsts) transformation computed by tree series transducers. Unless the used semiring is complete, this transformation is, in general, not wellde ned. In practice, many used semirings are not complete (like the probability semiring). We establish a syntactical condition that guarantees wellde nedness of the tsts transformation in arbitrary commutative semirings. For positive (i. e., zerosum and zerodivisor free) semirings the condition actually characterizes the wellde nedness, so that wellde nedness is decidable in this scenario. 1
Composing extended topdown tree transducers ∗
"... A composition procedure for linear and nondeleting extended topdown tree transducers is presented. It is demonstrated that the new procedure is more widely applicable than the existing methods. In general, the result of the composition is an extended topdown tree transducer that is no longer linea ..."
Abstract
 Add to MetaCart
A composition procedure for linear and nondeleting extended topdown tree transducers is presented. It is demonstrated that the new procedure is more widely applicable than the existing methods. In general, the result of the composition is an extended topdown tree transducer that is no longer linear or nondeleting, but in a number of cases these properties can easily be recovered by a postprocessing step. 1
Unidirectional Derivation Semantics for Synchronous TreeAdjoining Grammars ⋆
"... Abstract. Synchronous treeadjoining grammars have been given two types of semantics: one based on bimorphisms and one based on synchronous derivations, in both of which the input and output trees are constructed synchronously. We introduce a third type of semantics that is based on unidirectional d ..."
Abstract
 Add to MetaCart
Abstract. Synchronous treeadjoining grammars have been given two types of semantics: one based on bimorphisms and one based on synchronous derivations, in both of which the input and output trees are constructed synchronously. We introduce a third type of semantics that is based on unidirectional derivations. It derives output trees based on a given input tree and thus marks a first step towards conditional probability distributions. We prove that the unidirectional semantics coincides with the bimorphismbased semantics with the help of a strong correspondence to linear and nondeleting extended topdown tree transducers with explicit substitution. In addition, we show that stateful synchronous treeadjoining grammars admit a normal form in which only adjunction is used. This contrasts the situation encountered in the stateless case. 1