Inference systems for observation equivalences in the pi-calculus with recursion are proposed, and their completeness over the finite-control fragment with guarded recursions are proven. The inference systems consist of inference rules and equational axioms. The judgments are conditional equations which characterise symbolic bisimulations between process terms. This result on the one hand generalises Milner’s complete axiomatisation of observation equivalence for regular CCS to the pi-calculus, and on the other hand extends the proof systems of strong bisimulations for guarded regular pi-calculus to observation equivalences.
