The cooperation test [Apt, Francez & de Roever] was originally conceived to capture the proof theoretical analogue of distributed message exchange between disjoint processes, as opposed to the interference freedom test [Owicki & Gries], being the proof theoretical analogue of concurrent communication by means of interference through jointly shared variables. Some authors ([Levin & Gries, Lamport & Schneider, Schlichting and Schneider]) stress that both forms of communication can be proof theoretically characterized using interference freedom only, since proofs for both ultimately amount to an invariance proof of a big global assertion [Ashcroft], invariance of whose parts amounts to interference freedom. Yet I feel that the characteristic nature of the cooperation test is still preserved in the analysis of these authors, because in their analysis of CSP the part dealing with interference freedom specializes to maintenance of a global invariant, the expression of which requires per process the introduction of auxiliary variables which are updated in that process only, thus preserving the concept of disjointness (as opposed to sharing), since now all variables from different processes are disjoint. The cooperation test has been applied to characterize concurrent communication as occurring in Hoare's Communicating Sequential Processes (CSP) [Hoare 2], Ichbiah's ADA [ARM], and Brinch Hansen's Distributed Processes (DP) [Brinch Hansen]. This characterization has been certified through soundness and completeness proofs [Apt 2, Gerth]. As in the interference freedom test this characterization consists of two stages, a local sequential stage and a global stage.

Reactive systems are computing systems which are interactive, such as real-time systems, operating systems, concurrent systems, control systems, etc. They are among the most difficult computing systems to program. Temporal logic is a formal tool/language which yields excellent results in specifying reactive systems. This volume, the first of two, subtitled Specification, has a self-contained introduction to temporal logic and, more important, an introduction to the computational model for reactive programs, developed by Zohar Manna and Amir Pnueli of Stanford University and the Weizmann Institute of Science, Israel, respectively.

Concurrent systems abound in human experience but their fully adequate conceptualization as yet eludes our most able thinkers. The COSY (ConcurrentSystem) notation and theory was developed in the last decade as one of a number of mathematical approaches for conceptualizing and analyzing concurrent and reactive systems. The COSY approach extends theconventional notions of grammar and automaton from formal language and automata theory to collections of "synchronized" grammars and automata, permitting system specification and analysis of "true" concurrency without reduction to non-determinism. COSY theory is developed to a great level of detail and constitutes the first uniform and self-contained presentationof all results about COSY published in the past, as well as including many new results. COSY theory is used to analyze a sufficient number of typical problems involving concurrency, synchronization and scheduling, to allow the reader to apply the techniques presented tosimilar problems. The COSY model is also related to many alternative models of concurrency, particularly Petri Nets, Communicating Sequential Processes and the Calculus of Communicating Systems.