By considering graphs as logical structures, one...

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 ...

In this paper we give, for all constants k, l, explicit algorithms, that given a graph G = (V; E) with a tree-decomposition of G with treewidth at most l, decide whether the treewidth (or pathwidth) of G is at most k, and if so, find a tree-decomposition or (path-decomposition) of G of width at most k, and that use O(|V|) time. In contrast with previous solutions, our algorithms do not rely on non-constructive reasoning, and are single exponential in k and l. This result can be combined with a result of Reed [37], yielding explicit O(n log n) algorithms for the problem, given a graph G, to determine whether the treewidth (or pathwidth) of G is at most k, and if so, to find a tree- (or path-)decomposition of width at most k (k constant). Also, Bodlaender [13] has used the result of this paper to obtain linear time algorithms for these problems. We also show that for all constants k, there exists a polynomial time algorithm, that, when given a graph G = (V; E) with treewidth k, computes the pathwidth of G and a minimum path decomposition of G.

Diagram editors which are tailored to a specific diagram language typically support either syntax-directed editing or free-hand editing, i.e., the user is either restricted to a collection of predefined editing operations, or he is not restricted at all, but misses the convenience of such complex editing operations. This paper describes DiaGen, a rapid prototyping tool for creating diagram editors which support both modes in order to get their combined advantages. Created editors use hypergraphs as an internal diagram model and hypergraph parsers for syntactic analysis whereas syntax-directed editing is realized by programmed hypergraph transformation of these internal hypergraphs. This approach has proven to be powerful and general in the sense that it supports quick prototyping of diagram editors and does not restrict the class of diagram languages which it can be applied to. Key words: Diagram editors, rapid prototyping, hypergraph grammar, hypergraph transformation 1

The aim of the paper is to introduce the notion of a transformation unit together with its interleaving semantics and to study it as a means of constructing large graph transformation systems from small ones in a structured and systematic way. A transformation unit comprises a set of rules, descriptions of initial and terminal graphs, and a control condition. Moreover, it may import other transformation units for structuring purposes. Its semantics is a binary relation between initial and terminal graphs which is given by interleaving sequences. As a generalization of ordinary derivations, an interleaving sequence consists of direct derivation steps interleaved with calls of imported transformation units. It must obey the control condition and may be seen as a kind of structured derivation. The introduced framework is independent of a particular graph transformation approach and, therefore, it may enhance the usefulness of graph transformations in many contexts.

) Ugo Montanari and Francesca Rossi Universit`a di Pisa, Dipartimento di Informatica Corso Italia 40, 56125 Pisa, Italy E-mail: fugo,rossig@di.unipi.it Abstract. In this extended abstract we describe our approach to modelling the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. We use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are however combined by means of the synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. Moreover, to approach the problem of combining productions together, we suggest to exploit existing techniques for constraint solving. This is based on the observation that the combination pr...

. In this paper we describe an approach to model the dynamics of distributed systems. For distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. The basic idea is to use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are however combined by means of a synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. To formally model this kind of graph rewriting, however, we do not adopt the classical graph rewriting style but a more general framework, called the tile model, which allows for a clear separation between sequential rewriting and synchronization. Then, since the problem of satisfying the synchronization requirements may be a complex combinatorial pro...

We introduce a hypergraph-based process calculus with a generic type system. That is, a type system checking an invariant property of processes can be generated by instantiating the original type system. We demonstrate the key ideas behind the type system, namely that there exists a hypergraph morphism from each process graph into its type, and show how it can be used for the analysis of processes. Our examples are input/output-capabilities, secrecy conditions and avoiding vicious circles occurring in deadlocks. In order to specify the syntax and semantics of the process calculus and the type system, we introduce a method of hypergraph construction using concepts from category theory.

. A general framework for typing graph rewriting systems is presented: the idea is to statically derive a type graph from a given graph. In contrast to the original graph, the type graph is invariant under reduction, but still contains meaningful behaviour information. We present conditions, a type system for graph rewriting should satisfy, and a methodology for proving these conditions. In two case studies it is shown how to incorporate existing type systems (for the polyadic - calculus and for a concurrent object-oriented calculus) into the general framework. 1 Introduction In the past, many formalisms for the specication of concurrent and distributed systems have emerged. Some of them are aimed at providing an encompassing theory: a very general framework in which to describe and reason about interconnected processes. Examples are action calculi [18], rewriting logic [16] and graph rewriting [3] (for a comparison see [4]). They all contain a method of building terms (or ...

This paper presents a graph parsing approach to recognizing common, stereotypical computational structures, called clichés, in computer programs. Recognition is a powerful technique for efficiently reconstructing useful design information from existing software. We use a flow graph formalism, which is closely related to hypergraph formalisms, to represent programs and clichés and we use attributed flow graph parsing to automate recognition. The formalism includes mechanisms for tolerating variations in programs due to structure sharing (a common optimization in which a structural component is used to play more than one functional role). The formalism has also been designed to capture aggregation relationships on graph edges, which is used to encode aggregate data structure clichés and the abstract operations on them. A chart parsing algorithm is used to solve the problem of determining which clichés in a given cliché library are in a given program.