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By A. W. Roscoe

The easiest textbook for studying CSP. Dr. Hoare's unique e-book is sort of a reference. This e-book explains options method greater.

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Extra resources for The theory and practice of concurrency

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5. traces(P ✷ Q) = traces(P ) ∪ traces(Q) – this process offers the traces of P and those of Q. 6. traces(P Q) = traces(P ) ∪ traces(Q) – since this process can behave like either P or Q, its traces are those of P and those of Q. 7. traces( S) = {traces(P ) | P ∈ S } for any non-empty set S of processes. 8. 7 7 Technical note: The treatment of identifiers representing input values and process parameters, and appearing in boolean expressions, is very lightweight here. This treatment implicitly assumes that the only terms for which we want to compute traces(P ) are those with no free identifiers – so that for example any boolean expression must evaluate to true or false.

2 Recursion If we want to use a version of the process above which, instead of quickly stopping, can go on performing up, down indefinitely, we can use recursion. Two different processes which achieve this effect are defined by the equations P1 = up → down → P1 P2 = up → down → up → down → P2 The idea is that any use of the recursively defined process’s name (P1 or P2 ) on the right-hand side of the equations means exactly the same as the whole. It should be intuitively clear that any process satisfying either of these equations has the desired behaviour.

1) once the concepts they involve have been established. 2 Algebra One of our primary ways of understanding CSP will be to develop a set of algebraic laws which the operators satisfy. An algebraic law is the statement that two expressions, involving some operators and identifiers representing arbitrary processes (and perhaps other things such as events) are equal. By ‘equal’, we mean that the two sides are essentially the same: for CSP this means that their communicating behaviours are indistinguishable by the environment.

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