A Calculus of Mobile Processes – Note (1)

Abstract and Introduction

Abstract: We present the π-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen who added mobility to CCS while preserving its algebraic properties. The pi-calculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links.

After an illustrated description of how the π-calculus generalizes conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the pi-calculus of higher-order functions (the lambda-calculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. 

The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence indexed by distinctions -- i.e. assumptions of inequality among names. These theories are based upon a semantics in terms of a labelled transition system and a notion of strong bisimulation, both of which are expounded in detail in a companion paper. We also report briefly on work-in-progress based upon the corresponding notion of weak bisimulation, in which internal actions cannot be observed.

Note: For the first time I touch such a theoretic thesis, it really take me a lot of time to get the meaning. However, it also take me much excitement, moreover, it is a good beginning for me. In this abstract, the author tries to tell us what the π-calculus is in general. It is part of the communicating systems in which one can naturally express processes which have changing structure. The core concept I got from it is that the two neighbours in the communicating system can transmit the information that contains the changing-linkage data.

Question: What is the CCS algebra Model ?What does the process mean in this background, is this the common  process in the Operating System ?.

I Introduction

We present a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage.

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In such models(Actors model of Hewitt), mobility is often achieved by allowing processes to be passed as values in communication. we shall instead achieve it by allowing references to processes,  i.e. links to be communicated.

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Note: In this section, the author introduces the π-calculus, which, now I get, is an extension of CCS. It preserves CCS’s algebraic properties, as well as includes mobility.

Question: what is the relationship among the process, agents and the linkage ? Can I consider that agents are computers, while linkage link them , and the process represent the action and state of the communicating system ?

We suppose that an agent P wishes to send the value 5 to an agent R, along a link named a, and that R is willing to receive any value along that link. Then the appropriate flow graph is as follows:

                                          

Note: After the simple introduction, the author gives an example. In this graph, I can get the following info. P and R are agents, they are linked through the linkage a. P ≡ a’5.P’ and R ≡ a(x).R’, this is a definition. It means P sends the value 5 through port a and change to state P’ while R receive value x (any) and change to state R’. The system can be depicted like the following expression: (a’5.P’ | a(x).R’)/a. the post-fixed operator /a is called a restriction, which is one of the six kinds of the calculus discussing in the following section. Moreover, the author gives us another example to explain how the agent can send information that contains the changing-linkage data; in fact, it acts through sending the linkage itself. At last, the author discuss something about the expression of the calculus.

Question: Any engineering examples to this graph?