An Essay on General Grammars

Freund et al. introduced a framework of general sequential grammars. We study several aspects of this framework: (1) How to discuss accepting versus generating grammars in a general fashion. (2) How to integrate graph control within this framework. (3) We provide different multiset grammars as examples of this framework, leading us (for instance) to Petri nets and register machines. (4) We discuss insertion-deletion systems as yet another example, also combined with the other three already mentioned aspects.