Multi-way to two-way synchronization

A process P, in which an action on a gate a can be simultaneously performed by more than two subprocesses, is transformed in an "equivalent" process Q in which each action is performed at most by two subprocesses. That is, the degree of synchronization associated to QD should be at most 2. A variant of this problem imposes a bound on the synchronization degrees relative to a predefined subset of gates. Actually, the formal description of the problem and most of the solutions refer to a single multi-way gate present in P.