**6. Synchronizer and workflow logic**

P/T-systems will be used for the modelling of workflow logic. A synchronizer is a special place to connect transitions (tasks) with immediate successor relation (<).

To capture the fact that every task (transition) is executed (effectively) at most once for a single business case and workflow logic contains no iteration, a concept of restricted P/Tsystems, RP/T-systems for short, is proposed.

#### Definition 9

A P/T-system Σ=(S,T;F,K,W,M0) is a RP/T-system if it is acyclic (F+∩(F-1)+) =∅) and any transition is restricted to fire at most once. ◆

The P/T-system in Figure 2 is a good example: as a normal P/T-system, transition t2 can fire twice when p1 has 2 tokens; but as a RP/T-system, t2 can fire only once at the same marking. In fact, transitions t2 and t3 would fire when p1 has 2 tokens for a RP/T-system, though t2 remains enabled after its first firing.

Note that RP/T-systems are not a new class of net systems. If we introduce a control place c for every transition t such that c has an empty pre-set and {t} is its post-set, and initially it has one token. Apparently, with an added control place for every transition, every transition can fire at most once by conventional transition rules.
