By Matthew Hennessy
Disbursed platforms are quick changing into the norm in laptop technological know-how. Formal mathematical types and theories of disbursed habit are wanted with a purpose to comprehend them. This publication proposes a disbursed pi-calculus known as Dpi, for describing the habit of cellular brokers in a disbursed international. it truly is in keeping with an present 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 allotted platforms is built, within which the presence of sorts performs an enormous position. it's also proven how in precept this idea can be utilized to boost verification strategies for making certain the habit of dispensed brokers. The textual content is on the market to machine scientists with a minimum history in discrete arithmetic. It comprises an basic account of the pi-calculus, and the linked idea of bisimulations. It additionally develops the sort conception required by means of Dpi from first rules.
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Additional info for A Distributed Pi-Calculus
New b)(put! 6, b | b? (new r)(get! (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.
Print! y1 At this point there are three acknowledgements awaiting reception and no further communications along b, c or d are possible until at least some are delivered. In fact progress depends on the acknowledgement ack2 from the printer being delivered to the second forwarder; this will liberate the acknowledgement ack, which when delivered will in turn liberate ack1 , on which User1 is waiting. 4) where User2 represents (new ack2 ) b! (y1 , y2 )y2 ! | print! 4) above gives Sys4 −→∗ (User2 | FF | Print2 ) (Sys5 ) In Sys5 the user may send the second value, which eventually makes its way through the system, followed by a series of acknowledgements travelling in the opposite direction.
This is turn means that we have a bisimulation equivalence, denoted P ≈bis Q, between aPi processes. b actions. b would not expect Q to be able to perform an exact matching move Q ===⇒ Q . Instead we apply Barendregt’s convention, which dictates that this action should not be considered as b is not fresh to its context, since it appears free in Q. Thus the convention dictates that when the definition of bisimulation is applied to the processes P, Q, only actions whose bound names do not occur freely in P and Q are expected to be matched.
A Distributed Pi-Calculus by Matthew Hennessy