A Distributed Pi-Calculus by Matthew Hennessy

By Matthew Hennessy

Allotted platforms are quickly changing into the norm in desktop technology. Formal mathematical versions and theories of allotted habit are wanted with the intention to comprehend them. This e-book proposes a allotted pi-calculus known as Dpi, for describing the habit of cellular brokers in a allotted international. it truly is in keeping with an latest formal language, the pi-calculus, to which it provides a community layer and a primitive migration build. A mathematical concept of the habit of those allotted platforms is constructed, during which the presence of sorts performs an incredible function. it's also proven how in precept this thought can be utilized to improve verification recommendations for making certain the habit of allotted brokers. The textual content is out there to computing device scientists with a minimum history in discrete arithmetic. It comprises an hassle-free account of the pi-calculus, and the linked conception of bisimulations. It additionally develops the sort conception required through Dpi from first ideas.

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But note that the resulting pair P1 , P2 is not in S ; however it is in R, which is all that is required for the proof to go through. 21 In aPi, P1 ≈bis P2 implies P1 | Q ≈bis P2 | Q. Proof: This proof is somewhat more complicated. The relation consisting of all pairs of the form P1 |Q, P2 |Q such that P1 ≈bis P2 is not in general a bisimulation. We have to construct a more sophisticated one. Let R be the least relation that satisfies • P1 ≈bis P2 implies P1 , P2 ∈ R • P1 , P2 ∈ R implies P1 | Q, P2 | Q ∈ R for every process Q • P1 , P2 ∈ R implies (new n) P1 , (new n) P2 ∈ R for every name n.

7 Consider the process FF1 discussed above: FF1 ⇐ (new c)(F1 (b, c) | F1 (c, d )) The only possible reduction from this process is an unwinding of one of these recursive definitions. It is instructive to see how such a step can be inferred from the definition of the reduction relation −→. Recall that F1 (b, c) represents the recursive process rec z. (x) (c! (x) (c! (x) (c! x | z) is the body of the recursive definition. (x) (c! (x) (c! x | F1 (b, c)). So in summary one application of (r-unwind) gives F1 (b, c) −→ B(b, c) Let us now see how this reduction can take place as part of the larger system FF1 .

Here is how such a forwarder would look: F(b, c) ⇐ rec z. (x, y) (new ack)(c! () (y! | z)) A system forwarding values from b to d in order using such forwarders would be defined by: FF ⇐ (new c)(F(b, c) | F(c, d )) where F(c, d ) is obtained in the obvious manner from F(b, c). At this stage, before we give further examples that rely on the transmission of newly generated channels, it is best if we first define a formal semantics that will explain in detail how this mechanism works. Using this formal semantics we can then investigate the actual behaviour of processes such as FF, and see whether this 14 The asynchronous PI-CALCULUS in fact coincides with our intuitive understanding.

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