On the Complexity Aspects of Various Sub-classes of Linear Languages

The non-terminals in the underlying grammar play an important role in determining different characteristics of the language generated. The languages generated by the grammars are determined by a unique non-terminal known as the start symbol. Even without altering any of the production rules, the grammar produces a distinct language if we swap the start symbol for any other non-terminal. Occasionally, we purposefully include extra non-terminals to attain specific characteristics in both the grammar and parse trees. One such scenario is when we convert a language to Chomsky's Normal Form (CNF), in which case we add additional non-terminals to convert the parse tree into a binary tree. In this paper, we consider different sub classes of CFLs by restricting the number of nonterminals. We study different characteristics like the generative power of the grammar, the stack height, and the number of turns of the PDA which accept the languages produced by the grammars. We show that these characteristics are influenced by the number of nonterminals in the grammar.