On characterising strong bisimilarity in a fragment of CCS with replication

We provide a characterisation of strong bisimilarity in a fragment of CCS that contains only prefix, parallel composition, synchronisation and a limited form of replication. The characterisation is not an axiomatisation, but is instead presented as a rewriting system. We discuss how our method allows us to derive a new congruence result in the $pi$-calculus: congruence holds in the sub-calculus that does not include restriction nor sum, and features a limited form of replication. We have not formalised the latter result in all details.