By Matthew Hennessy
Disbursed structures are quickly turning into the norm in computing device technological know-how. Formal mathematical versions and theories of dispensed habit are wanted so that it will comprehend them. This booklet proposes a disbursed pi-calculus referred to as Dpi, for describing the habit of cellular brokers in a allotted global. it really is in response to an latest formal language, the pi-calculus, to which it provides a community layer and a primitive migration build. A mathematical conception of the habit of those disbursed structures is constructed, within which the presence of varieties performs a massive position. it's also proven how in precept this concept can be utilized to advance verification thoughts for ensuring the habit of dispensed brokers. The textual content is available to machine scientists with a minimum historical past in discrete arithmetic. It comprises an uncomplicated account of the pi-calculus, and the linked conception of bisimulations. It additionally develops the kind concept required by means of Dpi from first rules.
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Extra resources for A Distributed Pi-Calculus
9 Consider the forwarder from b to c, defined by F(b, c) ⇐ rec z. (x, y) (new ack)(c! (y! | z)) Such forwarders can be combined together as in the previous example but their use requires that an implicit protocol be followed. 1, consists of two forwarders linked together: FF ⇐ (new c)(F(b, c) | F(c, d )) The User sequentially supplies two values to the system, User ⇐ (new ack1 )(b! v1 , ack1 | ack 1 ? (new ack2 ) b! (x1 , x2 ) (x2 ! (y1 , y2 ) (y2 ! | print! (x, y) (new ack)(c! (y! | F(b, c))).
New n)(n? stop) stop ←→ (new n)(n? stop) P2 is not contextual. We could force it to be contextual, by considering the least relation R2 that contains R1 and is closed under static contexts. But is R2 now closed under observations? It turns out that this is indeed true although the proof is not straightforward. But it does emphasise that although our approach to defining semantic equivalences may be reasonable, in general it leads to relations that are very difficult to handle mathematically.
There are numerous cases and we only examine one, when µ is τ because of an output from P1 to Q . V . ˜ o (b)α Induction now gives a matching move from P2 , an action P2 ===⇒ P2 such that P1 , P2 ∈ R. We can combine this matching move with the complementary action τ ∗ ˜ from Q to give Q −→ (new b)(P 2 | Q ). This is the required matching move; the second, and more particularly the third, clause in the definition of R, ensures that ˜ P , (new b)(P 2 | Q ) ∈ R. 5 Contextual equivalences 37 • The final possibility is handled in a similar manner.
A Distributed Pi-Calculus by Matthew Hennessy