Conclusive Tree-Controlled Grammars

This paper presents a new approach to regulation of grammars. It divides the derivation trees generated by grammars into two sections—generative and conclusive (the conclusion). The former encompasses generation of symbols up till the moment when the lowest rightmost terminal of the derivation tree is generated, whereas the latter represents the final steps needed to successfully generate a sentence. A control mechanism based on regulating only the conclusion is presented and subsequently applied to tree-controlled grammars, creating conclusive tree-controlled grammars. As the main result, it is shown that the ratio between depths of generative and conclusive sections does not influence the generative power. In addition, it is demonstrated that any recursively enumerable language is generated by these grammars possessing no more than seven nonterminals while the regulating language is union-free.