Net Processes Correspond to Derivation Processes in Graph Grammars

Abstract The aim of this paper is to compare the running behaviour of Petri nets, given by firing sequences and processes, with derivations and derivation processes in graph grammars. In a first step, Petri nets are simulated by graph grammars so that each firing in a net corresponds exactly to a direct derivation in the simulating graph grammar. In a second step the non-sequential behaviour of nets described by net processes is related to the non-sequential behaviour of graph grammars given by derivation processes. a one-to-one correppondence can be established between the processes on a Petri net and the complete conflict-free processes in the graph grammar simulating the net. This adds a new piece of evidence substantiating the close relationship between net and graph grammar theory.