Conclusive Tree-Controlled Grammars

TL;DR

This paper introduces conclusive tree-controlled grammars that regulate the final derivation steps, showing they can generate any recursively enumerable language with limited nonterminals and that their power is unaffected by the depth ratio of derivation sections.

Contribution

It proposes a novel regulation approach focusing on the conclusion of derivations, expanding the class of tree-controlled grammars with new generative capabilities.

Findings

The depth ratio of generative and conclusive sections does not affect generative power.

Any recursively enumerable language can be generated with at most seven nonterminals.

The regulating language in these grammars is union-free.

Abstract

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.