By Matthew Hennessy
Dispensed platforms are speedy changing into the norm in laptop technological know-how. Formal mathematical versions and theories of disbursed habit are wanted in an effort to comprehend them. This publication proposes a dispensed pi-calculus referred to as Dpi, for describing the habit of cellular brokers in a allotted international. it's in keeping 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 dispensed platforms is built, during which the presence of sorts performs an important position. it's also proven how in precept this concept can be utilized to increase verification concepts for ensuring the habit of disbursed brokers. The textual content is on the market to computing device scientists with a minimum history in discrete arithmetic. It includes an uncomplicated account of the pi-calculus, and the linked conception of bisimulations. It additionally develops the sort idea required by way of Dpi from first rules.
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Additional info for A Distributed Pi-Calculus
Z | s! z | g) | rec p. (z) (y! | s! x | p)) 26 The asynchronous PI-CALCULUS The initial value is set to 0. There are then two methods for accessing the cell: • To obtain the current value the user must send along the access channel get a return channel that is bound to the variable y. The current value is read from s and sent to the user along the return channel. In addition the value is reinstated in the local store s. • To change the value of the cell a user must send the new value, which will be bound to x, and an acknowledgement channel, to be bound to y.
In aPi users can only interact with processes by communicating on channels, and these interactions form the basis of the definition of ≈bis . Consequently we would expect that bisimulation equivalence will imply whatever semantic equivalence based on user interaction that emerges. Nevertheless, there is still room for discussion on what this more basic notion of equivalence should be. As a first attempt we could say that two processes are distinguishable only if there is some action that one can perform and the other cannot; a priori a user could then discern a difference by asking for this action to be performed.
1. It presupposes a set Names of names, ranged over by n, m, . . , a, b, c . . for communication channels or resources. We also use a set Vars of variables, place-holders for values that can be transmitted via the communication channels. , ranged over by bv, but more importantly channel names themselves. We will reserve the meta-variable u for identifiers, that is either names or variables. The intuitive meaning of each of the syntactic constructs is as follows: • The simplest possible process, which does nothing, is represented by the term stop.