Petri Net Controlled Grammars: the Case of Special Petri Nets

A Petri net controlled grammar is a context-free grammar equipped with a Petri net, whose transitions are labeled with rules of the grammar or the empty string, and the associated language consists of all terminal strings which can be derived in the grammar and the the sequence of rules in every terminal derivation corresponds to some occurrence sequence of transitions of the Petri net which is enabled at the initial marking and finished at a final marking of the net. We present some results on the generative capacity of such grammars so that the associated Petri nets are restricted to some known special classes of Petri nets.