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 look-ahead 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 look-ahead, 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 look-ahead 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 ...

. 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 finite-copying top-down 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 Hyperedge-replacement graph grammars, also called context-free hypergraph grammars, are well-studied devices for the generation of graph and hypergraph languages (see, e.g., [Hab92, Eng97, DHK97]). Their basic operation is the replacement of a non-terminal hypered...

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.

We introduce the bottom-up tree-to-graph transducer, which is very similar to the usual (total deterministic) bottom-up 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 tree-to-graph transducer is said to be tree-generating and naturally defines a tree-to-tree translation. We prove that bottom-up tree-to-graph transducers define the same tree-to-tree translations as the previously introduced top-down tree-to-graph transducers. This is in contrast with the well-known incomparability of the usual bottom-up and top-down tree transducers.

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 top-down direction, it still cannot do it in a bottom-up direction since it is restricted to return only a single tree and such tree cannot be decomposed once created. In this paper, we introduce multi-return 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 top-down and bottom-up 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 multi-return extension: (1) in the deterministic case, the expressive powers of these two coincide (2) in the nondeterministic case (with the call-by-value evaluation strategy) multi-return macro tree transducers are strictly more expressive. 1.

. The power of top-down, bottom-up, and tree-to-graphto -tree transducers (tgt transducers) to compute translations from hyperedge-replacement algebras into edge-replacement algebras is investigated. Compositions of top-down and bottom-up tree transducers are too weak if the operations in the target algebra are powerful enough to define all series-parallel graphs, 2-trees, 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 so-called 2tree operations, which are generalizations of the well-known operations to generate 2-trees. 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 concept of context-free hypergraph grammars (cfhg grammars) has been studied extensively over the past decade. In this paper we introduce attributed context-free hypergraph grammars (acfhg grammars) as an extension of cfhg grammars. An acfhg grammar consists of an underlying context-free 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. Also we show that 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 semantics with programs of some programming ...

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 call-by-need reduction. 1

Abstract. We introduce top-down deterministic transducers with rational lookahead (transducer for short) working on infinite terms. We show that for such a transducer T, there exists an MSO-transduction T such that for any graph G, unfold(T (G)) = T (unfold(G)). Reciprocally, we show that if an MSO-transduction T “preserves bisimilarity”, then there is a transducer T such that for any graph G, unfold(T (G)) = T (unfold(G)). According to this, transducers can be seen as a complete method of implementation of MSO-transductions that preserve bisimilarity. One application is for transformations of equational systems. 1

in.Kuehnemann@inf.tu-dresden.de ffl Dr. rer. nat. Walter Nauber Tel.: (+49) 351 - 463 8293 E-mail: Walter.Nauber@inf.tu-dresden.de Scientific Staff: ffl Sebastian Maneth M.Sc./Univ. of Massachusetts (supported by DFG; from July 1st) Tel.: (+49) 351 - 463 8374 E-mail: Sebastian.Maneth@inf.tu-dresden.de ffl Dr.-Ing. Lutz Rudiger Tel.: (+49) 351 - 463 8487 E-mail: Lutz.Ruediger@inf.tu-dresden.de ffl Dipl.-Math. Rainer Vater Tel.: (+49) 351 - 463 8293 E-mail: Rainer.Vater@inf.tu-dresden.de Annual Report 1997 3 Scholars of the DFG (German Research Foundation) ffl Dipl.-Inf. Daniel Kirsten Tel.: (+49) 351 - 463 8253 E-mail: Daniel.Kirsten@inf.tu-dresden.de ffl Dipl.-Inform. Markus Lohrey (until November 30th) Tel.: (+49) 351 - 463 8253 E-mail: Markus.Lohrey@inf.tu-dresden.de Scientific Auxiliary ffl Dipl.-Inf. Bernd Jokubeit (from Februa