Process Algebra with Timing by J.C.M. Baeten

By J.C.M. Baeten

This ebook is anxious with a couple of theories that may be used for describ­ ing and reading platforms of interacting elements in case it's fascinating or essential to regard their time-dependent habit. Society is changing into an increasing number of depending on complicated machine­ dependent structures which are composed of numerous elements that act at the same time and engage - to synchronize and speak with one another. The com­ plexity of those structures arises to a good volume from the various ways that their parts can have interaction. the necessity that those elements act and in­ teract on time to boot provides significantly to the complexity. In constructing this sort of procedure, it is very important have the ability to collect a greater knowing of the suitable matters on the conceptual point, to explain the process in an actual approach at numerous degrees of aspect, and to research it at the foundation of the descriptions. whilst the early algebraic theories approximately approaches, resembling ACP [16, 17, 20], CCS [49, 50] and CSP [27, 39], have been constructed for that goal, the confirmed opinion used to be nonetheless that timing is a priority which could normally be taken care of independently. it truly is for this reason now not fabulous that timing is intentionally missed in these theories. they've got now all been prolonged to accommodate timing.

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After that, S goes back to waiting for another message. The process R waits until a frame with a message p( m) is offered at its internal port (port 4). When a frame is offered, R consumes it, unpacks it, and then delivers the message m at its external port (port 2) and a frame with 1. No Timing 22 an acknowledgement p( ack) at its internal port. After that, R goes back to waiting for another frame. The process C simply passes on frames between the internal ports of S and R, in both directions.

2. Each of the three processes is recursively specified by a single equation: S L = r 1 (m) · s 3(p(m)) · r3(p(ack)) · s 1 (ack) · S, mEM L r4(p(m)) · s2(m) · s4(p( ack)) · R, R= C = mEM L r 3(p(m)) · s4(p(m)) · C + r4(p(ack)) · s 3(p(ack)) ·C. mEM The whole message-passing system is described by the following term: 8H(S II R I C) ' where H = {si(f) I i E {3,4},! E F} U {ri(f) I i E {3,4},! E F}. , the extension of BPA with parallel composition and encapsulation. The formal presentation of ACP is given in this subsection.

4. We consider a simple timer. The timer is set at a certain time period when a request for it is offered at its input port (port 1). From the moment that this time period expires, the timer can produce a onceonly notification at its output port (port 2) until it receives the next request. The expiration notification is delayable till the next request to anticipate the situation where the requesting process is not ready to receive it promptly. The time period at which the timer is set must be less than 24 hours and the time unit used is the minute.

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