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 ha
s exactly one behaviour. A component behaviour is represented by a stream p
rocessing function. We introduce operations on behaviours and lift them to
specifications leading to mt 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 al
gebraic and logical basis for state automata specifications and state trans
ition diagrams. (C) 2000 Elsevier Science B.V. All rights reserved.