Axiomatising Real-Time Processes

In this paper, we present a relativised compositional proof system for real-timed processes. The proof system allows us to derive statements of the form A ⊢ E = F, where processes E, F may contain free time variables and A is a formula of the first order theory of time domain. The formula A ⊢ E = F means that A is a condition for process E to be bisimilar to process F. The proof system is sound and is independent of the choice of time domain, allowing time to be discrete or dense. It is complete for finite terms, i.e. terms without recursion, over dense time domains. It is also shown complete for a sublanguage over discrete time domains. We discuss how to restrict occurrences of time variables to obtain the sublanguage. We finally discuss extensions of the proof system for recursively defined processes.