A timed model for communicating sequential processes

Abstract

The parallel language CSP [9], an earlier version of which was described in [7], has become a major tool for the analysis of structuring methods and proof systems involving parallelism. The significance of CSP is in the elegance by which a few simply stated constructs (e.g., sequential and parallel composition, nondeterministic choice, concealment, and recursion) lead to a language capable of expressing the full complexity of distributed computing. The difficulty in achieving satisfactory semantic models containing these constructs has been in providing an adequate treatment of nondeterminism, deadlock, and divergence. Fortunately, as a result of an evolutionay development in [S], [lo], [15], [l], [14], [2], and [4] we now have several such models. The purpose of this paper is to report the development of the first real-time models of CSP to be compatible with the properties and proof systems of the abovementioned untimed models. Our objective in this development is the construction of a timed CSP model which satisfies the following: (1) Continuous with respect to time. The time domain should consist of all nonnegative real numbers, and there should be no lower bound on the time difference between consecutive observable events from two processes operating asynchronously in parallel. (2) Realistic. A given process should engage in only finitely many events in a bounded period of time. (3) Continuous and distributive with respect to semantic operators. All semantic operators should be continuous, and all the basic operators as defined in [2], except recursion, should distribute over nondeterministic choice. (4) Verijiable design. The model should provide a basis for the definition, specification, and verification of time critical processes with an adequate treatment of nondeterminism, which assists in avoidance of deadlock and divergence.