Expressing First-Order π-Calculus in Higher-Order Calculus of Communicating Systems

In the study of process calculi, encoding between different calculi is an effective way to compare the expressive power of calculi and can shed light on the essence of where the difference lies. Thomsen and Sangiorgi have worked on the higher-order calculi (higher-order Calculus of Communicating Systems (CCS) and higher-order π-calculus, respectively) and the encoding from and to first-order π-calculus. However a fully abstract encoding of first-order π-calculus with higher-order CCS is not available up-today. This is what we intend to settle in this paper. We follow the encoding strategy, first proposed by Thomsen, of translating first-order π-calculus into Plain CHOCS. We show that the encoding strategy is fully abstract with respect to early bisimilarity (first-order π-calculus) and wired bisimilarity (Plain CHOCS) (which is a bisimulation defined on wired processes only sending and receiving wires), that is the core of the encoding strategy. Moreover from the fact that the wired bisimilarity is contained by the well-established context bisimilarity, we secure the soundness of the encoding, with respect to early bisimilarity and context bisimilarity. We use index technique to get around all the technical details to reach these main results of this paper. Finally, we make some discussion on our work and suggest some future work.