## Comparing the Expressive Power of the Synchronous and the Asynchronous pi-calculus

Comparing the Expressive Power of the Synchronous and the Asynchronous pi-calculus
The Asynchronous pi-calculus, as recently proposed by Boudol and, independently, by Honda and Tokoro, is a subset of the pi-calculus which contains no explicit operators for choice and output-prefixing. The communication mechanism of this calculus, however, is powerful enough to simulate output-prefixing, as shown by Boudol, and input-guarded choice, as shown recently by Nestmann and Pierce. A natural question arises, then, whether or not it is possible to embed in it the full pi-calculus. We show that this is not possible, i.e. there does not exist any uniform, parallel-preserving, translation from the pi-calculus into the asynchronous pi-calculus, up to any â€œreasonableâ€ notion of equivalence. This result is based on the incapablity of the asynchronous pi-calculus of breaking certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the pi-calculus and CCS.
Quite an important result for those who care about pi.

The others may just enjoy the use of symmetry in the proof.

As CiteSeer is down this weekend, I used a link to CiteBase.

[on edit: CiteSeer is back]

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### A follow-up

What Is a Good' Encoding of Guarded Choice?

The pi-calculus with synchronous output and mixed-guarded choices is strictly more expressive than the pi-calculus with asynchronous output and no choice. As a corollary, Palamidessi recently proved that there is no fully compositional encoding from the former into the latter that preserves divergence-freedom and symmetries. This paper shows that there are nevertheless good' encodings between these calculi.

In detail, we present a series of encodings for languages with (1) input-guarded choice, (2) both input- and output-guarded choice, and (3) mixed-guarded choice, and investigate them with respect to compositionality and divergence-freedom. The first and second encoding satisfy all of the above criteria, but various `good' candidates for the third encoding|inspired by an existing distributed implementation|invalidate one or the other criterion. While essentially confirming Palamidessi's result, our study suggests that the combination of strong compositionality and divergence-freedom is too strong for more practical purposes.