A Distributed Pi-Calculus by Matthew Hennessy

By Matthew Hennessy

Allotted platforms are quick turning into the norm in computing device technological know-how. Formal mathematical versions and theories of dispensed 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 allotted global. it's in response to 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 disbursed structures is built, within which the presence of varieties performs a massive position. it's also proven how in precept this thought can be utilized to increase verification recommendations for ensuring the habit of allotted brokers. The textual content is on the market to desktop scientists with a minimum heritage in discrete arithmetic. It includes an simple account of the pi-calculus, and the linked idea of bisimulations. It additionally develops the sort concept required by way of Dpi from first rules.

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V ˜ • If P −−−−→ Q then P is structurally equivalent to (new b)(c! V | Q). (X ) R). • If P − −→ Q then P is structurally equivalent to a term of the form (new b)(P ˜ ∩ n(V ) = ∅, and Q is structurally equivalent to (new b)(P ˜ where (b) | R{|V/X |}). τ • P− → Q implies P −→ Q. V inference of the actions P − −−→ Q and P − −→ Q. The final statement, which is the most interesting, is also by induction on the τ inference of P −→ Q. If this is an instance of the axioms (l-eq), (l-neq) or (l-unwind) then the result is immediate since these axioms are also used in the definition of reduction.

X) (c! x | z); we will use this device extensively. Two such forwarding processes can be run in parallel, as for example in FF1 ⇐ (new c)(F1 (b, c) | F1 (c, d )) where F1 (c, d ) is given by F1 (c, d ) ⇐ rec z. (x) (d ! x | z) In the system FF1 the two concurrent processes F1 (b, c) and F1 (c, d ) share a common local channel c along which they may communicate. F1 (b, c) can input a value along b and make it available to F1 (c, d ) at channel c; F1 (c, d ), on receipt of the value, may in turn make it available at d .

6 (contexts) The set of (static) contexts for aPi is the least set of extended terms such that • – is a static context • if C[−] is a static context then so are C[−] | Q and Q | C[−] for every process Q • if C[−] is a static context then so is (new n) C[−] for every name n. Note that every static context contains exactly one occurrence of the marker −. For any process P we let C[P] denote the process that results from syntactically replacing the occurrence of − with P in C[−]. 1; here names that are free in P may become bound when placed in the context C[−].

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