Expressiveness of point-to-point versus broadcast communications

Abstract

In this paper we address the problem of the expressive po- wer of point-to-point communication to implement broadcast communication. We demonstrate that point-to-point communication as in CCS [M89] is “too asynchronous” to implement broadcast communication as in CBS [P95]. Milner’s π-calculus [M91] is a calculus in which all communications are point-to-point. We introduce bπ-calculus, using broadcast instead of rendez-vous primitive communication, as a variant of value-passing CBS in which communications are made on channels as in Hoare’s CSP [H85] — and channels can be transmitted too as in π-calculus — but by a broadcast protocol: processes speak one at a time and are heard instantaneously by all others. In this paper, using the fact that π-calculus enjoys a certain interleaving property, whereas bπ-calculus does not, we prove that there does not exist any uniform, parallel-preserving translation from bπ-calculus into π-calculus, up to any “reasonable” equivalence. Using arguments similar to [P97], we also prove a separation result between CBS and CCS.