π-Calculus, internal mobility, and agent-passing calculi

Abstract

The π-calculus is a process algebra which originates from CCS and permits a natural modelling of mobility (i.e., dynamic reconfigurations of the process linkage) using communication of names. Previous research has shown that the π-calculus has a much greater expressiveness than CCS, but it also has a much more complex mathematical theory. The primary goal of this work is to understand the reasons for this gap. Another goal is to compare the expressiveness of name-passing calculi, i.e., calculi like π-calculus where mobility is achieved via exchange of names, and that of agent-passing calculi, i.e., calculi where mobility is achieved via exchange of agents. We divide the mobility mechanisms of the π-calculus into internal and external mobility mechanisms. The study of the subcalculus which only uses internal mobility, called πI, suggests that internal mobility is responsible for much of the expressiveness of the π-calculus, whereas external mobility is responsible for many of the semantic complications. A pleasant property of πI is the full symmetry between input and output constructs. Internal mobility is strongly related to agent-passing mobility. By imposing bounds on the order of the types of πI and of the Higher-Order π-calculus ( Sangiorgi, 1992) we define a hierarchy of name-passing calculi based on internal mobility and one of agent-passing calculi. We show that there is an exact correspondence, in terms of expressiveness, between the two hierarchies.