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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.