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Re: Pi-Calculus Model question.

From: Assaf Arkin <arkin@intalio.com>
Date: Mon, 14 Apr 2003 09:38:57 -0700
Message-ID: <3E9AE421.8050401@intalio.com>
To: Ricky Ho <riho@cisco.com>
CC: public-ws-chor@w3.org

Ricky Ho wrote:

> Assaf, thanks for your detail explanation of the Pi-C model.  I have 
> some following questions.
> 1) Can a channel have more than one listening process ?

Receiving a message over a channel is something an action does. So you 
may want to have different actions listening to the same channel at 
different points in times.

If you are talking about broadcast, then you would model it differently 
by either talking to distinct listeners over different channels, or 
expressing infinite number of indistinct listeners using one channel.

But these are all formalisms of a lower-level language. A lower-level 
language may take a multicast protocol like IP multicast and express it 
in terms of distinct channels, e.g. representing MAC addresses. In a 
higher-level language you'll simplify that by having a multicast 
capability which yields to that formalism but is easier to work with.

> 2) How to do reduction when "condition" steps are involved ?  Are the 
> following reducible ?
> Process placeorder
>   Send order
>   Receive orderResponse
> Process acceptOrder
>   Receive order
>   switch
>     case conditionX
>       Send orderResponse
>     default
>       Send errorResponse

Nope. You end up at a point where one send can be reduced with one 
receive. But you have another send that can happen and nothing to reduce 
it with.

> 3) So far, each steps within a process is sequential.  Can a process 
> have multiple steps in parallel ?  If so, can you give me an example 
> ?  And how reduction will be done in this case ?

Do you mean multiple different steps or multiple instances of the same step?

If you mean different steps than I've already shown that. Remember that 
nothing interesting happens on its own, all the interesting things 
happen concurrently. To receive a message someone also have to send it. 
So the first example I gave contained two things that happen in parallel 
and you can extend it to 3, 4, etc. However complex it is, you can 
easily express it.

If you mean the same step occuring n times in parallel, then #4 gives an 
example for that.

As for showing the reduction, this is where pi-c becomes more 
complicated than elementary school algebra and you'll have to start 
looking into congruence, simulation, bi-simulation, etc. I'm not 
mathematically inclined, so I can't give you a much better explanation 
that you can find in Milner's book.

> 4) Can you give me a loop example ?  I vaguely recall you can use a 
> recursive definition to achieve that.


until = send:start | ! ( receive:start.doSomething.(send:start[x=y]0) )

The ! (bang) precedes a process that can happen n times (0 to infinity) 
whenever it's guard is able to receive a message. So !P = !P | P = !P | 
P | P = P | P | P ... It's also called replication and represents the 
ability to do the same thing n times. For example, a Web server that 
receives an HTTP request and sends back a response does the same thing n 

The [x=y] is some shorthand for evaluating a condition. If the condition 
is false you do the process on the left, if it's true you do the process 
on the right (kind of like if ... else ... ).

So in this case you have a loop that is performed at least once, if x=y 
it ends, and if x!=y it repeats, essentially an until loop, and it 
repeats itself without recursion.


> Best regards,
> Ricky
Received on Monday, 14 April 2003 12:40:54 UTC

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