Grammars Controlled by Petri Nets with Place Capacities

A Petri net controlled grammar is a grammar equipped with a Petri net whose transitions are labeled with production rules and nonterminals of the grammar, 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. In the paper we investigate the generative power of grammars controlled by Petri nets with place capacities.