By Matthew Hennessy
Dispensed structures are quick changing into the norm in laptop technological know-how. Formal mathematical versions and theories of dispensed habit are wanted with a view to comprehend them. This booklet proposes a dispensed pi-calculus known as Dpi, for describing the habit of cellular brokers in a allotted 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 built, within which the presence of sorts performs a huge function. it's also proven how in precept this thought can be utilized to enhance verification thoughts for making certain the habit of disbursed brokers. The textual content is on the market to machine scientists with a minimum heritage in discrete arithmetic. It comprises an undemanding account of the pi-calculus, and the linked conception of bisimulations. It additionally develops the sort concept required by way of Dpi from first rules.
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Extra info for A Distributed Pi-Calculus
P, Q have the form P1 | Q , P2 | Q , respectively, and P1 , P2 ∈ R. Here induction will ensure that every move from P1 can be matched by a move from P2 . µ The proof proceeds by rule induction on the derivation of the action P −→ P . 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 ).
The move from P is determined by a move from P1 , induction gives a matching move from P2 , which in turn gives the required matching move from Q. 21 will show P1 ≈bis P2 implies Q |P1 ≈bis Q |P2 . With some more work we could also prove that it is also preserved by the other constructs in the language. But the static operators are sufficient for our purposes. 5 Contextual equivalences We have seen that ≈bis is an excellent behavioural equivalence for aPi: • it is bisimulation based, and therefore has associated with it powerful coinductive proof techniques • it is contextual, and therefore appropriate for a compositional approach to process verification.
X) print! x ))) One can show that the composite system Client2 | Mem will reduce to essentially one stable state, namely print! 6 | Mem In all of the examples seen so far systems have been described in terms of their components, together with communication channels, between them. 3 An action semantics for aPi 27 generated dynamically on demand. But aPi can also describe systems in which the connectivity, that is the sharing of communication channels between processes, can vary arbitrarily. For example consider the following server, for providing forwarders between channels: GenF ⇐ rec w.
A Distributed Pi-Calculus by Matthew Hennessy