Parallel Composition - A practical solution

A digital system exhibits a specific circuit structure and behavior. There are diverse methods of modeling structure and behavior, while manifold related to each other. In this paper we present a formalism to achieve an Automata Based theory for Composition (ABC) to model circuit structures in a unique manner. This means that the modeling automaton itself is unique for a given circuit structure (up to isomorphisms, e.g. alternative naming, symmetry). We get success on this approach by using a novel automata based parallel composition for discrete event systems named simultaneously-parallel composition. This composition establishes to automatically synthesize basic circuit entities to an overall circuit model, by preserving two axioms, synchronicity and asynchronicity. It is very suited to model and abstract complex hybrid systems with high safety and security issues. In addition, we show a novel representation of the behavior of the composed automata, embedding the states and transitions into open (2D) and closed (3D) diamonds, and discuss several theoretical and practical aspects.