One of the objections to the use of Petri nets or, equivalently, specifications written in the COSY (Concurrent Systems) notation, for modelling realistic systems is that they would grow too large to be of any practical use. Generators for the concise representation of large (possibly infinite) structures in net theory or specifications in COSY are traced to their origins in Carl Adam Petri’s thesis [P62]. The generators implemented in the current version of COSY and its accompanying simulation and analysis tools are presented in detail together with design decisions which led to their present form.