Processes as formal power series: A coinductive approach to denotational semantics

We characterize must testing equivalence on CSP in terms of the unique homomorphism from the Moore automaton of CSP processes to the final Moore automaton of partial formal power series over a certain semiring. The final automaton is then turned into a CSP-algebra: operators and fixpoints are defined, respectively, via behavioural differential equations and simulation relations. This structure is then shown to be preserved by the final homomorphism. As a result, we obtain a fully abstract compositional model of CSP phrased in purely set-theoretical terms.