Generation of Languages by Rewriting Systems that Resemble Automata

This paper introduces and discusses #-rewriting systems, which represent language-generating devices that resemble automata by using finitely many states without any nonterminals. It demonstrates that these systems characterize the well-known infinite hierarchy of language families resulting from programmed grammars of finite index in a very natural way. In its conclusion, this paper suggests some variants of #-rewriting systems.