The Asynchronous π-calculus, proposed by Honda and Tokoro (1991) and , independently, by Boudol (1992), is a subset of the π-calculus (Milner et al., 1992) 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 π-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 π-calculus into the asynchronous π-calculus, up to any "reasonable" notion of equivalence. This result is based on the incapability of the asynchronous π-calculus to break certain symmetries possibly present in the initial communication graph. By similar arguments, we prove a separation result between the π-calculus and CCS, and between the π-calculus and the π-calculus with internal mobility, a subset of the π-calculus proposed by Sangiorgi where the output actions can only transmit private names.
For example, in REF the author proves that there exists no reasonable encoding from the π-calculus to the asynchronous π-calculus by showing that the symmetric leader election problem has no solution in the asynchrnous version of the π-calculus.
Comparing the Expressive Power of the Synchronous and the Asynchronous pi-calculi
Mathematical Structures in Computer Science, 13(5) , 685-719, 2003
Mathematics Computer Science