Structurally and Arithmetically Controlled Grammars

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