Unique Parallel Decomposition in Branching and Weak Bisimulation Semantics

We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that infinite behaviours may fail to have parallel decompositions at all. Then, we prove that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Finally, we establish that weakly bounded behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids.