The intention of this paper is to extend our generic component framework presented at FASE 2002 [4] to a specific kind of connector architectures similar to architectural connections in the sense of Allen and Garlan [1]. In our generic component framework we have considered components with explicit import, export and body parts connected by embeddings and transformations and composition of components with a compositional transformation semantics. Our framework, however, was restricted to components with a single import and export interface. Here we study architectures based on connectors with multiple imports and components with multiple exports. Architectures studied in this paper are built up from components and connectors in a noncircular way. The semantics of an architecture is defined by reduction step sequences in the sense of graph reductions. The main result shows existence and uniqueness of the semantics of an architecture as a normal form of reduction step sequences. Our generic framework is instantiated on one hand to connector architectures based on CSP as the formal specification technique in the approach by Allen and Garlan. On the other hand it is instantiated to connector architectures based on high-level-replacement systems in general and Petri nets in particular. A running example using Petri nets as modeling technique illustrates all concepts and results.

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We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. A dilating technique for these diagrams, which can be used for any degree of the digraph, is applied to generate the digraphs of the family. Moreover, two infinite families of digraphs with distinguished metric properties will be given using these methods. The first family contains digraphs with asymptotically large ratio between the order and the diameter as the degree increases (moreover it is the first known asymptotically dense family). The second family, for fixed degree d = 3, contains digraphs with the current best known density.Peer ReviewedPostprint (author's final draft

Abelian Cayley digraphs can be constructed by using a generalization to Z n of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, have asymptotically large number of vertices as the diameter increases. Up to now, the best known asymptotically dense results were all non-constructive.