Abstract
Petri nets are becoming one of the most important mathematical tools in Computer Science. In this paper we propose a new firing strategy in Petri Nets called a parallel firing strategy and study some mathematical properties of concurrent grammars which are controlled by Petri nets under parallel firing strategies. We propose some modes on this strategy and a notion of concurrent context-free grammar which is a similar to the context-free Petri nets under parallel firing strategy, where parallel firing modes of context-free Petri nets were converted to rule applications in context-free grammars. Moreover, we investigate some their properties.
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