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

1 COMETE - Concurrency, Mobility and Transactions
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : The Asynchronous $\pi$-calculus, proposed by Honda and Tokoro (1991) and, independently, by Boudol (1992), is a subset of the $\pi$-calculus \cite{Milner:92:IC} 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 Honda and Tokoro (1991) and by Boudol (1992), and input-guarded choice, as shown by Nestmann and Pierce (2000). A natural question arises, then, whether or not it is as expressive as the full $\pi$-calculus. We show that this is not the case. More precisely, we show that there does not exist any uniform, fully distributed translation from the $\pi$-calculus into the asynchronous $\pi$-calculus, up to any ''reasonable'' notion of equivalence. This result is based on the incapability of the asynchronous $\pi$-calculus to break certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the $\pi$-calculus and CCS, and between the $\pi$-calculus and the $\pi$-calculus with internal mobility, a subset of the $\pi$-calculus proposed by Sangiorgi where the output actions can only transmit private names.
Document type :
Journal articles

https://hal.inria.fr/inria-00201104
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Submitted on : Sunday, December 23, 2007 - 6:10:07 PM
Last modification on : Thursday, January 20, 2022 - 5:29:35 PM
Long-term archiving on: : Tuesday, April 13, 2010 - 3:32:17 PM

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### Citation

Catuscia Palamidessi. Comparing the Expressive Power of the Synchronous and the Asynchronous pi-calculi. Mathematical Structures in Computer Science, Cambridge University Press (CUP), 2003, 13 (5), pp.685-719. ⟨10.1017/S0960129503004043⟩. ⟨inria-00201104⟩

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