Algebraic Specification of Reactive Systems

We present an algebraic method for the specification of reactive distributed systems. We introduce basic operators on specifications making the set of specifications into a specification algebra. This allows us to work with an algebra of system specifications in analogy to the process algebras that provide algebras of reactive programs. However, in contrast to process algebras we work with a concrete representation (a mathematical system model) of specifications and use algebaric equations to specify components and not programming languages. A specification is represented by a predicate that describes a set of behaviors. A deterministic component has exactly one behavior. A behavior is represented by a stream processing function. We introduce operations on behaviors and lift them to specifications. We show how algebraic system specifications can be used as an algebraic and logical basis for state automata specifications and state transition diagrams.