On Synchronous and Asynchronous Mobile Processes Paola Quaglia 1⋆ and David Walker 2 1 Aethra Telecomunicazioni, Italy 2 Oxford University Computing Laboratory, U.K. Abstract. This paper studies the relationship between synchronous and asynchronous mobile processes, in the setting of the π-calculus. A type system for processes of the asynchronous monadic subcalculus is intro- duced and used to obtain a full-abstraction result: two processes of the polyadic π-calculus are typed barbed congruent iff their translations into the subcalculus are asynchronous-monadic-typed barbed congruent. 1 Introduction This paper studies the relationship between synchronous and asynchronous mo- bile processes, in the setting of the π-calculus [MPW92, Mil99]. A primitive of the π-calculus, inherited from its ancestor CCS [Mil89], is a form of handshake communication. The (polyadic) π-term x〈a 1 a 2 〉.P expresses a process that may send the pair of names a 1 ,a 2 via the link named x and continue as P , and the term x(y 1 y 2 ).Q a process that may receive a pair of names via x (a reader unfa- miliar with π-calculus may care to refer to section 2). Interaction between these processes is expressed by x〈a 1 a 2 〉.P | x(y 1 y 2 ).Q −→ P | Q{ a1a2 / y1y2} , where { a1a2 / y1y2} indicates substitution of the as for the ys in Q. The fact that interaction is expressed by handshake communication is important for the tractability of the π-calculus, and that of many other theories of concurrent systems that are based on communication primitives of a similar nature. On the other hand, many concurrent systems, especially distributed systems, use forms of asynchronous communication, in which the act of sending a datum and the act of receiving it are separate. Relatedly, many languages for pro- gramming concurrent or distributed systems have asynchronous primitives, an important reason for this being that they are amenable to efficient implementa- tion. Language features for synchronized communication are often implemented using asynchronous primitives. The π-calculus has a subcalculus in which communication may be understood as asynchronous [HT91, Bou92]. The key step in achieving this is the decree that in the subcalculus, the only output-prefixed terms are those of the form x〈a〉. 0, ⋆ This work was done while the author was at BRICS, Aarhus University, Denmark. J. Tiuryn (Ed.): FOSSACS 2000, LNCS 1784, pp. 283–296, 2000. c  Springer-Verlag Berlin Heidelberg 2000