A Bridge between CSP Processes and Functional Automata

This entry develops the Proc-Omata framework on top of HOL-CSP and its extensions. Proc-Omata are defined from functional automata and come in four variants: deterministic, terminating deterministic, non-deterministic, and terminating non-deterministic. This subclass of processes combines the expressiveness of CSP with automata-like structure (reachability, enableness), making it particularly amenable to invariant-based reasoning. We lift sequential composition and synchronization product to the automata level through combination functions and prove compactification theorems that enable reasoning over large process architectures. An essential ingredient is the use of restriction spaces, which guarantees well-defined fixed points even in the non-deterministic setting. Finally, we illustrate the applicability of the framework with the Dining Philosophers, where compactification yields proofs that scale to an arbitrary finite but unbounded number of participants in this parameterized process architecture.