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Re: Pi-Calculus Model question.

From: Ricky Ho <riho@cisco.com>
Date: Tue, 15 Apr 2003 01:17:40 -0700
Message-Id: <4.3.2.7.2.20030415011651.02a4cbd0@franklin.cisco.com>
To: Steve Ross-Talbot <steve@enigmatec.net>
Cc: Assaf Arkin <arkin@intalio.com>, public-ws-chor@w3.org

I mean listening the channel at the same time and it is clear that this is 
not allowed.

Rgds, Ricky

At 09:27 PM 4/14/2003 +0100, Steve Ross-Talbot wrote:
>Ricky,
>
>when you say can they share the same channel do you mean can they do this 
>at the same time (i.e. multicast or pub/sub) or do you mean can they share 
>the same channel one after the other?
>
>Cheers
>
>Steve T
>
>On Monday, April 14, 2003, at 06:55  pm, Ricky Ho wrote:
>
>>
>>Assaf, thanks a lot for elaboration.  I have some more questions embedded.
>>
>>
>>At 09:38 AM 4/14/2003 -0700, Assaf Arkin wrote:
>>
>>>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.
>>
>>I'm thinking the 3-party scenario  P | Q | R.  Can there be two parties 
>>listening on the same channel ?
>>
>>By reading the example, I observe that
>>1) All "send" operation can be reduced
>>2) An "receive" operation can be reduced if it can find a concurrent 
>>matched "send" operation.
>>
>>So if there are multiple "receive" from more than one party, which one 
>>will be received ?  I expect multiple channel listening (at the same 
>>time) should NOT be allowed.  But I want to confirm with you the actual answer.
>>
>>
>>>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.
>>
>>Lets introduce two more roles, "Airplane Shipper" and "Truck Shipper", 
>>each has its own process flow.
>>
>>There are two cases here.
>>
>>1) Queue scenario
>>The seller send a "shipment request" to a channel.  Can both Shippers 
>>listening on this same channel but only one of them will successfully 
>>receive it ?  Lets say the seller doesn't care and both shippers are 
>>competing to get the shipment request.
>>
>>2) Broadcast scenario
>>The seller send a "shipment request" to a channel.  Can both Shippers 
>>listening on this same channel and both receive it ?
>>
>>In this example, since only one shipper will get the shipment request 
>>while the other one will just wait but never gets it.  Is the composition 
>>process still reducible to 0 | 0 | 0 | 0 ?
>>
>>
>>>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.
>>
>>Does it match now if I change to ..
>>
>>Process placeorder
>>   Send order
>>   Choice
>>     Case 1
>>       Receive orderResponse
>>     Case 2
>>       Receive errorResponse
>>
>>Process acceptOrder
>>   Receive order
>>   switch
>>     case conditionX
>>       Send orderResponse
>>     default
>>       Send errorResponse
>>
>>If so, how does the "choice/receive" match with "switch/send" ?
>>
>>
>>>>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.
>>
>>I mean multiple different steps but from the same process (party).
>>For example, lets say the seller in parallel send one shipment request to 
>>the airplane shipper and another shipment request to the truck 
>>shipper.  And then he wait for both respond and then select one with a 
>>cheaper price before proceed to next step.  How do you represent the 
>>"synchronization" after two parallel steps ?
>>
>>
>>>If you mean the same step occuring n times in parallel, then #4 gives an 
>>>example for that.
>>
>>#4 shows the same step occuring n times "sequentially" but not "in 
>>parallel".  Right ?
>>
>>Rgds, Ricky
>>
>>
>>>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.
>>>
>>>Reflexive.
>>>
>>>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 times.
>>>
>>>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.
>>>
>>>arkin
>>>
>>>>
>>>>Best regards,
>>>>Ricky
>>
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Received on Tuesday, 15 April 2003 04:17:55 UTC

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