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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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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 ...
Output String Languages of Compositions of Deterministic Macro Tree Transducers
 Leiden University
, 2001
"... 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 restr ..."
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Cited by 7 (5 self)
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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 twoway generalized sequential machine. Similar results hold for attributed tree transducers, for controlled EDT0L systems, and for YIELD mappings (which proves properness of the IOhierarchy). Witnesses for the properness of the macro tree transducer hierarchy can already be found in the latter three hierarchies.
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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. 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...
The Equivalence of BottomUp and TopDown TreetoGraph Transducers
 J. COMPUT. SYST. SCI
, 1996
"... We introduce the bottomup treetograph transducer, which is very similar to the usual (total deterministic) bottomup tree transducer except that it translates trees into hypergraphs rather than trees, using hypergraph substitution instead of tree substitution. If every output hypergraph of the tr ..."
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Cited by 7 (4 self)
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We introduce the bottomup treetograph transducer, which is very similar to the usual (total deterministic) bottomup tree transducer except that it translates trees into hypergraphs rather than trees, using hypergraph substitution instead of tree substitution. If every output hypergraph of the transducer is a jungle, i.e., a hypergraph that can be unfolded into a tree, then the treetograph transducer is said to be treegenerating and naturally defines a treetotree translation. We prove that bottomup treetograph transducers define the same treetotree translations as the previously introduced topdown treetograph transducers. This is in contrast with the wellknown incomparability of the usual bottomup and topdown tree transducers.
MultiReturn Macro Tree Transducers
 PLANX
, 2008
"... Macro tree transducers are a simple yet expressive formal model for XML transformation languages. The power of this model comes from its accumulating parameters, which allow to carry around several output tree fragments in addition to the input tree. However, while each procedure is enabled by this ..."
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Cited by 6 (1 self)
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Macro tree transducers are a simple yet expressive formal model for XML transformation languages. The power of this model comes from its accumulating parameters, which allow to carry around several output tree fragments in addition to the input tree. However, while each procedure is enabled by this facility to propagate intermediate results in a topdown direction, it still cannot do it in a bottomup direction since it is restricted to return only a single tree and such tree cannot be decomposed once created. In this paper, we introduce multireturn macro tree transducers as a mild extension of macro tree transducers with the capability of each procedure to return more than one tree at the same time, thus attaining symmetry between topdown and bottomup propagation of information. We illustrate the usefulness of this capability for writing practically meaningful transformations. Our main technical contributions consists of two formal comparisons of the expressivenesses of macro tree transducers and its multireturn extension: (1) in the deterministic case, the expressive powers of these two coincide (2) in the nondeterministic case (with the callbyvalue evaluation strategy) multireturn macro tree transducers are strictly more expressive. 1.
The Use of Tree Transducers to Compute Translations Between Graph Algebras
 Graph Grammars and their Application to Computer Science, LNCS 1073
, 1996
"... . The power of topdown, bottomup, and treetographto tree transducers (tgt transducers) to compute translations from hyperedgereplacement algebras into edgereplacement algebras is investigated. Compositions of topdown and bottomup tree transducers are too weak if the operations in the target ..."
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. The power of topdown, bottomup, and treetographto tree transducers (tgt transducers) to compute translations from hyperedgereplacement algebras into edgereplacement algebras is investigated. Compositions of topdown and bottomup tree transducers are too weak if the operations in the target algebra are powerful enough to define all seriesparallel graphs, 2trees, or related types of graphs. Tgt transducers are shown to be more powerful. These are able to compute translations into ER algebras whose operations are socalled 2tree operations, which are generalizations of the wellknown operations to generate 2trees. 1 Introduction Using the notion of hyperedge replacement a hypergraph H may be understood as an operation on hypergraphs (see [3]). If H contains hyperedges e 1 ; : : : ; e n it represents an operation that takes n argument hypergraphs H 1 ; : : : ; Hn and yields the hypergraph obtained by the substitution of H i for e i (1 i n). Roughly speaking, this means...
The substitution vanishes
 In Algebraic Methodology and Software Technology, Proceedings, volume 4019 of LNCS
, 2006
"... Abstract. Accumulation techniques were invented to transform functional programs, which intensively use append functions (like inefficient list reversal), into more efficient programs, which use accumulating parameters instead (like efficient list reversal). In this paper we present a generalized an ..."
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Abstract. Accumulation techniques were invented to transform functional programs, which intensively use append functions (like inefficient list reversal), into more efficient programs, which use accumulating parameters instead (like efficient list reversal). In this paper we present a generalized and automatic accumulation technique that also handles programs operating with unary functions on arbitrary tree structures and employing substitution functions on trees which may replace different designated symbols by different trees. We show that this transformation does not deteriorate the efficiency with respect to callbyneed reduction. 1
Attributed ContextFree Hypergraph Grammars
 JOURNAL OF AUTOMATA, LANGUAGES, AND COMBINATORICS
, 1997
"... The concept of contextfree hypergraph grammars (cfhg grammars) has been studied extensively over the past decade. In this paper we introduce attributed contextfree hypergraph grammars (acfhg grammars) as an extension of cfhg grammars. An acfhg grammar consists of an underlying contextfree hypergra ..."
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Cited by 2 (2 self)
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The concept of contextfree hypergraph grammars (cfhg grammars) has been studied extensively over the past decade. In this paper we introduce attributed contextfree hypergraph grammars (acfhg grammars) as an extension of cfhg grammars. An acfhg grammar consists of an underlying contextfree hypergraph grammar G 0 and an attribution which associates attributes with the nonterminal symbols of G 0 analogous to the classical attribute grammars (ag's) by Knuth. We show that acfhg grammars and ag's are closely related in such a way that an ag can be used to compute the attribute values of an acfhg grammar. Due to this relationship the known techniques for attribute evaluation for ag's can be exploited for acfhg grammars. Several known concepts such as compatible functions and attributed tree grammars can be embedded into the concept of acfhg grammars, provided an appropriate semantics is associated with the acfhg grammar. Finally, we show how an acfhg grammar can be used to associate semanti...
On the expressiveness of deterministic transducers over infinite trees
 In Proceedings of the 21st Annual Symposium on Theoretical Aspects of Computer Science (STACS), volume 2996 of LNCS
, 2004
"... Abstract. We introduce topdown deterministic transducers with rational lookahead (transducer for short) working on innite terms. We show that for such a transducer eT, there exists an MSOtransduction T such that for any graph G, unfold(T (G)) = eT (unfold(G)). Reciprocally, we show that if an M ..."
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Abstract. We introduce topdown deterministic transducers with rational lookahead (transducer for short) working on innite terms. We show that for such a transducer eT, there exists an MSOtransduction T such that for any graph G, unfold(T (G)) = eT (unfold(G)). Reciprocally, we show that if an MSOtransduction T \preserves bisimilarity", then there is a transducer eT such that for any graph G, unfold(T (G)) = eT (unfold(G)). According to this, transducers can be seen as a complete method of implementation of MSOtransductions that preserve bisimilarity. One application is for transformations of equational systems. 1
Semirings and TreetoGraphtoTree Transductions
, 1995
"... It is shown that topdown tree transducers are as powerful as sharingfree treetograph totree transducers as far as the computation of functions is considered whose codomain is a semiring. ..."
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It is shown that topdown tree transducers are as powerful as sharingfree treetograph totree transducers as far as the computation of functions is considered whose codomain is a semiring.