The Universal Process

TL;DR

This paper defines and constructs a universal process in process calculus, enabling higher order communication and embedding recursion theory, with implications for security protocols and programming languages.

Contribution

It formally defines universal processes in process calculus and demonstrates their construction, integrating recursion theory into process models.

Findings

Universal process can be formally defined and constructed.

Embedding recursion theory into process calculus is feasible.

Potential applications include higher order communication and security protocols.

Abstract

A universal process of a process calculus is one that, given the G\"{o}del index of a process of a certain type, produces a process equivalent to the encoded process. This paper demonstrates how universal processes can be formally defined and how a universal process of the value-passing calculus can be constructed. The existence of such a universal process in a process model can be explored to implement higher order communications, security protocols, and programming languages in the process model. A process version of the S-m-n theorem is stated to showcase how to embed the recursion theory in a process calculus.