In: Proc. of First European GETGRATS Workshop. October 1997.
Abstract: In software engineering one of the main issues is structuring. As well horizontal - composing and decomposing a system - as vertical structuring - stepwise refinement of a system - are essential for the development of large and complex systems. In this paper we transfer well-known structuring techniques for horizontal and vertical structuring, namely union and transformation to abstract statecharts [EGKP97] and action nets. Especially, we provide full proofs for the corresponding results in [EGKP97]. The construction of unions and transformations is based on high-level replacement systems, a categorical generalization of graph grammars and a general categorical description for high-level structures. Interesting examples are algebraic specifications, graph grammars, hypergraph grammars, low- and high-level Petri nets among others [EHKP91]. Hence, we investigate the category of action nets and of abstract statecharts. Both categories do not have pushouts in general, but only for specific morphisms. Nevertheless, this is sufficient to define unions and transformations, to consider this category as an instance of high-level replacement systems, and to recover the important compatibility results for union and transformation.
Keywords: Statecharts, Petri nets, transformation systems, horizontal and vertical structuring.