By Matthew Hennessy

ISBN-10: 0511275641

ISBN-13: 9780511275647

ISBN-10: 0521873304

ISBN-13: 9780521873307

Dispensed structures are quickly turning into the norm in desktop technology. Formal mathematical types and theories of allotted habit are wanted with a view to comprehend them. This ebook proposes a allotted pi-calculus referred to as Dpi, for describing the habit of cellular brokers in a dispensed international. it truly is in line with an latest formal language, the pi-calculus, to which it provides a community layer and a primitive migration build. A mathematical thought of the habit of those disbursed platforms is constructed, during which the presence of sorts performs a massive function. it's also proven how in precept this idea can be utilized to boost verification recommendations for ensuring the habit of disbursed brokers. The textual content is on the market to desktop scientists with a minimum history in discrete arithmetic. It comprises an hassle-free account of the pi-calculus, and the linked concept of bisimulations. It additionally develops the kind conception required by way of Dpi from first ideas.

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**Additional resources for A Distributed Pi-Calculus**

**Example text**

1 below. if v1 = v2 then R1 else R2 is a test for the identity of simple values. R1 | R2 represents two processes running in parallel; they may exchange values using input/output on channels. (new n) R is a scoping mechanism for names. For example in the process R1 | (new n) R2 the name n is known to R2 but not to R1 ; of course names are values and so in the course of a computation n may be made known to R1 as the result of a communication; this will be referred to as the scope extrusion of the name n.

Note that this terminal state is stable; there is no further reduction that can be made from it. There are slight variations in the possible computations starting from the initial state Sys1 , essentially caused by the unwinding of recursive definitions. But it is possible to prove that • all are finite; they must end in a stable state, from which no further reductions are possible • all these stable states are structurally equivalent to (FF1 | print! v ). 8 (syntactic abbreviations) When writing processes we assume that the input and restriction operator binds more strongly than parallel composition.

W, x ) as only the place-holders for incoming values have been changed. (y, z) (d ! y, x | b! (z, w) (d ! z, x | b! w, x ) In a similar manner, assuming m does not appear in P, (new n)(c! (x) P) ≡α (new m)(c! (x) (P{|m/n|})) We will identify terms up to α-equivalence, or more formally use terms as representatives of their α-equivalence classes. 4 (Barendregt) This identification of terms up to α-equivalence allows us to use a very convenient convention when writing terms. We will always ensure all bound identifiers are distinct, and chosen to be different from all free identifiers.

### A Distributed Pi-Calculus by Matthew Hennessy

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