(Come) puoi modellare le trasmissioni nel pi-calculus?

Puoi modellare trasmissioni affidabili nel pi-calculus?

Se é cosi, come?

In caso contrario: ci sono algebre di processo simili in cui è possibile?

Cosa ho provato:

Se il mittente desidera inviare un messaggio y a tutti i P 1 a P n , è possibile scrivere ! ( ¯ x y ) . S e x ( z ) . Da P 1 a x ( z ) . P n . Ma come si garantisce che ( ¯ x y ) venga replicato n volte, ovvero che nessun messaggio si perda? non lo so$S$$y$$P_1$$P_n$
$\overline{x}y).S$$x(z).P_1$$x(z).P_n$$(\overline{x}y)$$n$$n$in anticipo. È (solo) possibile con l'invio di più messaggi avanti e indietro tra tutti i processi coinvolti?

... o fraintendo il comportamento non deterministico della replica?

$\pi$$n$$n$$n$$n$ (or more) separate message exchanges, which have intermediate states (e.g. the sender has sent messages to 100 receivers, and needs to send another 150). A context can observe, interact and interfere with these intermediate states, which is not possible with the atomic broadcast messages. To deal with this shortcoming of $\pi$-calculus (or indeed any calculus based on point-to-point message passing), Ene and Muntean propose a broadcasting variant b$\pi$ [2, 3], based on earlier work by Prasad on CBS, a variant of CCS with broadcasting [4].

More technically, [1] calls an encoding $e$ reasonable if the following is the case.

• The encoding preserves parallel composition, i.e. $e(P|Q) = e(P) | e(Q)$.
• The encoding preserves injective renaming, i.e. $e(P\sigma) = e(P)\sigma$ for any injective renaming $\sigma$.
• The encoding satisfies some technical conditions about the preservation of input and output actions, see [1] for details.

Then [1] shows that no reasonable encoding from b$\pi$ to $\pi$ can exist. They establish this separation result using a variant of Palamidessi's electoral systems proof technique [5].

There has been work on this subject since [1-4] were published, e.g. by M. Hennessy, but those are the pioneering papers.

As an aside, broadcast is usually understood as one sender communicating with many receivers, but it is also possible to generalise point-to-point communication in the other direction where you have one receiver synchronising with multiple senders (this is used in e.g. Petri nets), or hybrid forms of both. I. Phillips has established a separation result that shows that this form of broadcasting can also not be encoded in $\pi$-calculus. I am not sure whether this result is published or not.

[1] C. Ene, T. Muntean, Expressiveness of Point-to-Point versus Broadcast Communications.

[2] C. Ene, T. Muntean, A Broadcast-based Calculus for Communicating Systems.

[3] C. Ene, T. Muntean, Testing theories for Broadcasting Processes.

[4] K. V. S. Prasad, A Calculus of Broadcasting Systems.

[5] C. Palamidessi, Comparing the Expressive Power of the Synchronous and the Asynchronous $\pi$-calculi.