Algebraic specification of reactive systems

We present an algebraic method for the equational specification of reactive distributed systems. We define a mathematical concept of specifications of reactive components in terms of predicates. A component specification is a predicate that describes a set of behaviours. A deterministic component has exactly one behaviour. A component behaviour is represented by a stream processing function. We introduce operations on behaviours and lift them to specifications leading to an algebra of system specifications in analogy to the process algebras that provide algebras of reactive programs. However, in contrast to the purely axiomatic description of process algebras we use algebraic equations to specify components and not to formalise composition operators. We show how algebraic system specifications can be used as an algebraic and logical basis for state automata specifications and state transition diagrams.