Formal Development of Concurrent Systems using Algebraic High-Level Nets and Transformations

In this paper we present algebraic high-level nets: a combination of algebraic specifications and Petri nets. Algebraic specifications are used to specify the data-structure and Petri nets to specify the data-flow. This combination is a very powerful description technique. Moreover we introduce net transformations, net fusions and net unions as structuring techniques. Fusions and unions can be considered as horizontal structuring mechanisms in the sense that we combine nets to obtain a new net consisting of the given components. Fusions capture the notion of sharing of subnets, while unions are kinds of net composition. Net transformations are based on concepts from graph grammars because net refinements are defined via productions. Transformations can be seen as high-level vertical refinements. Moreover we show compatibility between these techniques, i.e. in our framework vertical refinement and horizontal structuring of nets are compatible.