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# A Calculus of Distributed and Parallel Processes by Clemens H. Cap

By Clemens H. Cap

This e-book introduces a technique calculus for parallel, allotted and reactive structures. It describes the conceptual foundations in addition to the mathematical concept at the back of a programming language, and a couple of software examples. the selected strategy presents a framework for realizing the semantics of parallel and disbursed structures. additionally, it may be without delay utilized to sensible difficulties.

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Extra resources for A Calculus of Distributed and Parallel Processes

Example text

4b Xl ~b X2~b··· and state Xk E Sb, for which t is enabled by fs(X k ), the following condition holds: If XI is a state with I > k, so that t is enabled by fs(Xd and t is different from all tk, tk+l, ... ,tl-l, then t is still enabled by fs(X I ).

34 Chapter 2. Transition Systems of all events. Such a theory would not adequately reflect the day-to-day experiences with distributed systems. Special relativity theory tells us that it is not always possible to determine which of the two events a and b occured earlier [MTW73a]. A process theory which is based on the present form of transition systems is therefore in contradiction to an established physical theory of time. I the speed of light. This is not true. Computers circling the earth in satellites and space shuttles presently are used for navigational purposes and require a precise time base.

The reason behind this is that a transition system approach will always place transition b before c and d, between c and d, or after c and d. If we implement this process on a distributed system in a way that b executes on one processor, and c and d on another, then it is impossible to say, whether b was executed before c and d, in between, or after both. A faithful model of this process should therefore lead to an order relation in which b cannot be compared to c and d. The intended relation is the intersection of - and at the same time the coarsest relation compatible with - all obtained ...