Generation of Languages by Rewriting Systems That Resemble Automata

Abstract

This paper introduces and discusses ^-rewriting systems, which represent languagegenerating 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.

Regulated Grammars and Automata

“…5.4) represent a classical grammatical model of regulation, which has been covered in this monograph in detail. On the other hand, #-rewriting systems have been introduced relatively recently (see [80,81,83,85,87]). These systems generate languages just like any grammars.…”

“…On the other hand, like regulated automata, they use simple state-based regulation during their language-generation process. These systems characterize an infinite hierarchy of language families resulting from programmed grammars of finite index (see [85]). As a result, to put it from a broader perspective, regulated systems of this combined kind are naturally related to some classical results about formal languages, on which they can shed light in an alternative way.…”