Structurally and arithmetically controlled grammars

Over the quarter century, it is gratifying to note that the significance of regulated or controlled grammars (i.e. grammars with regulated rewriting) has been recognized by many parties where it has been used widely in a great variety of scientific disciplines ranging from Linguistics through DNA Computing up to the Informatics and recently come to Big Data Analytics. Therefore, literally we can find hundreds of studies of well-known of various types of controlled grammars and their investigation have amount to a thrilling trend within formal language theory. Given the extensive literature on issues related to controlled grammars, this research focused on arithmetically controlled grammars and tree controlled grammars, which are practically important. Thereby, in this paper, we briefly recapitulate the background of formal language theory and highlight the key results of multiset grammars, valence grammars and tree controlled grammars. In this paper, a new controlled grammar that can be generated using both control mechanisms together is proposed for future research.