By Matthew Hennessy
Dispensed platforms are quick changing into the norm in computing device technological know-how. Formal mathematical types and theories of dispensed habit are wanted in an effort to comprehend them. This publication proposes a disbursed pi-calculus known as Dpi, for describing the habit of cellular brokers in a allotted 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 idea of the habit of those allotted structures is constructed, during which the presence of sorts performs an immense function. it's also proven how in precept this idea can be utilized to boost verification suggestions for making certain the habit of allotted brokers. The textual content is offered to machine scientists with a minimum history in discrete arithmetic. It comprises an simple account of the pi-calculus, and the linked idea of bisimulations. It additionally develops the sort conception required via Dpi from first rules.
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Extra info for A Distributed Pi-Calculus
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. • The term c!
Proof: Let S be the set of all pairs (new n) P1 , (new n) P2 such that P1 ≈bis P2 and let R be S ∪ ≈bis . The result follows if we can show that R is a bisimulation. This however is not very difficult as every action from (new n) P is determined by an action from P. 36 The asynchronous PI-CALCULUS Note however that R must include ≈bis . This is because processes of the form (new n) R may extrude n as part of an output action. For example one (n)αo possible action from (new n) P1 is (new n) P1 −−−→ P1 , where αo is an output αo action P1 −→ P1 .
Pn and define our semantic equivalence to be the largest equivalence relation between processes that satisfies all of them. In other words processes will be distinguished only if it is required by one of our desirable properties. 22 (observations) Let P ⇓barb c if P ===⇒ P , for some P , (b) value V . We say a relation R over processes preserves observations if P, Q ∈ R implies P ⇓barb c if and only if Q ⇓barb c for every name c. This notion of observation is easy to justify. We can design a simple test that will determine if a process can perform such an observation.
A Distributed Pi-Calculus by Matthew Hennessy