Attributed Tree Transducers Research Articles

Characterizing attributed tree translations in terms of macro tree transducers

It is well known that attributed tree transducers can be equipped with “regular look-around” in order to obtain a more robust class of translations. We present two characterizations of this class in terms of macro tree transducers (MTTs): the first one is a static restriction on the rules of the MTTs, where the MTTs need to be equipped with regular look-around. The second characterization is a dynamic one, where the MTTs only need regular look-ahead.

A pumping lemma for output languages of attributed tree transducers

A pumping lemma for output languages of attributed tree transducers

Composing Stack-Attributed Tree Transducers

Stack-attributed tree transducers extend attributed tree transducers with a pushdown stack device for attribute values, which make them strictly more powerful. This paper presents an algorithm for the composition of stack-attributed tree transducers with attributed tree transducers. The algorithm is an extension of the existing method to compose attributed tree transducers. It leads to some natural closure properties of the corresponding classes of tree transformations.

Output String Languages of Compositions of Deterministic Macro Tree Transducers

The composition of total deterministic macro tree transducers gives rise to a proper hierarchy with respect to their output string languages (these are the languages obtained by taking the yields of the output trees). There is a language not in this hierarchy which can be generated by a (quite restricted) nondeterministic string transducer, namely, a two-way generalized sequential machine. Similar results hold for attributed tree transducers, for controlled EDT0L systems, and for YIELD mappings (which proves properness of the IO-hierarchy). Witnesses for the properness of the macro tree transducer hierarchy can already be found in the latter three hierarchies.

A Comparison of Tree Transductions Defined by Monadic Second Order Logic and by Attribute Grammars

Two well-known formalisms for the specification and computation of tree transductions are compared: the mso graph transducer and the attributed tree transducer with look-ahead, respectively. The mso graph transducer, restricted to trees, uses monadic second order logic to define the output tree in terms of the input tree. The attributed tree transducer is an attribute grammar in which all attributes are trees; it is preceded by a look-ahead phase in which all attributes have finitely many values. The main result is that these formalisms are equivalent, i.e., that the attributed tree transducer with look-ahead is an appropriate implementation model for the tree transductions that are specifiable in mso logic. This result holds for mso graph transducers that produce trees with shared subtrees. If no sharing is allowed, the attributed tree transducer satisfies the single use restriction.

Domains of partial attributed tree transducers

The domains of partial attributed tree transducers (patt's) are the tree languages recognized by tree walking automata in universal acceptance mode. Moreover, the domains of patt's having monadic output are the tree languages recognized by deterministic tree walking automata.

The Universality of Higher-Order Attributed Tree Transducers

In this paper we present higher-order attributed tree transducers as a formal computational model for higher-order attribute grammars. The latter is a generalization of the classical concept of attribute grammars in the sense that during attribute evaluation, the input tree can be enlarged by inserting subtrees which were computed during attribute evaluation. We prove the universality of this formalism by showing that the class of functions described by higher-order attributed tree transducers coincides with the class of (partial) recursive tree functions.

A Characterization of Attributed Tree Transformations by a Subclass of Macro Tree Transducers

We present a characterization of the class of tree transformations computed by (noncircular) attributed tree transducers, in terms of a subclass of macro tree transducers, called attributed-like macro tree transducers. In fact, we prove formally that attributed tree transducers and attributed-like macro tree transducers generate the same class of tree transformations. Moreover, we prove that it is decidable whether a macro tree transducer is attributed-like.

The Generating Power of Total Deterministic Tree Transducers

Attributed tree transducers are abstract models used to study properties of attribute grammars. One abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input, instead of derivation trees of a context-free grammar. In this paper we show that with respect to the generating power this is not an abstraction; i.e., we show that attributed tree transducers and attribute grammars generate the same class of term (or tree) languages. To prove this, a number of results concerning the generating power of top-down tree transducers are established, which are interesting in their own. We also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes. The latter result is achieved by proving a hierarchy of classes of tree languages generated by context-free hypergraph grammars with respect to their rank.

Attributed Tree Transducers Cannot Induce All Deterministic Bottom-up Tree Transformations

In this paper we give a deterministic bottom-up tree transducer T and show that the tree transformation τ( T ) induced by it can be induced by no attributed tree transducer.

Synthesized and inherited functions

In this paper we introduce a new formal model for the concept of syntaxdirected semantics, calledmacro attributed tree transducer (for short: mat tree transducer). This model is based on (noncircular) attributed tree transducers and on macro tree transducers. In the first type of transducer, semantic values are computed by means of meaning names called synthesized attributes, and by means of context names called inherited attributes. Both, synthesized and inherited attributes represent basic semantic values. In the second type of transducer, semantic values are computed by meaning names only which are called states. However, in order to have a means of handling context information, states represent functions over semantic values. The new model integrates attributed tree transducers and macro tree transducers by allowing both, meaning names and context names to represent functions over semantic values. In analogy to the terminology of attributed tree transducers, we call such meaning names and context names also synthesized functions and inherited functions, respectively. We present an inductive characterization of the tree transformation computed by an mat tree transducer. We prove that mat tree transducers are more powerful than both, attributed tree transducers and macro tree transducers. We characterize mat tree transducers by the two-fold composition of attributed tree transducers. This characterization has three consequences: (1) the height of output trees of mat tree transducers is bounded exponentially in the size of the input tree, (2) the composition hierarchy of mat tree transducers is strict, and (3) mat tree transducers are closed under right-composition with top-down tree transducers, but not under left-composition. Moreover, we prove that the addition of inherited attributes does not increase the computational power of macro tree transducers.

Synthesized and inherited functions - a new computational model for syntax-directed semantics

In this paper we introduce a new formal model for the concept of syntax-directed semantics, called macro attributed tree transducer (for skort: mat tree transducer). This model is based on (noncircular) attributed tree transducers and on macro tree transducers. In the first type of transducer, semantic values are computed by means of meaning names called synthesized attributes, and by means of context names called inherited attributes. Both, synthesized and inherited attributes represent basic semantic values. In the second type of transducer, semantic values are computed by meaning names only which are called states. However, in order to have a means of handling context information, states represent functions over semantic values

Tree transducers with external functions

In this paper we investigate the computational power of particular tree transducers, viz., macro tree transducers and attributed tree transducers. The former tree transducers formalize the idea of syntax-directed translation, with the possibility of handling context; the latter tree transducers can serve as a formal model for the reduction semantics of attribute grammars. Here we generalize these tree transducers by allowing the invocation of external functions during the usual rewriting process. The main result of this paper is the characterization of macro tree transducers with external function calls in terms of attributed tree transducers with external function calls. Furthermore, such tree transducers with external function calls induce, in an obvious way, two operators on the set of all classes of tree functions. According to this point of view, we define two classes of tree functions inductively in the same way as the class PREC of primitive recursive tree functions, except that the closure under the scheme of primitive recursion is replaced by the closure under macro tree transducers with external function calls and attributed tree transducers with external function calls, respectively. As a second result of this paper we prove that these two classes are equal to PREC.