LL (1) Parser versus GNF inducted LL (1) Parser on Arithmetic Expressions Grammar: A Comparative Study

The prime objective of the proposed study is to determine the induction of Greibach Normal Form (GNF) in Arithmetic Expression Grammars to improve the processing speed of conventional LL(1) parser. Conventional arithmetic expression grammar and its equivalent LL(1) is used in the study which is converted. A transformation method is defined which converts the selected grammar into a Greibach normal form that is further converted into a GNF based parser through a method proposed in the study. These two parsers are analyzed by considering 399 cases of arithmetic expressions. During statistical analysis, the results are initially examined with the Kolmogorov-Smirnov and Shapiro-Wilk test. The statistical significance of the proposed method is evaluated with the Mann-Whitney U test. The study described that GNF based LL(1) parser for arithmetic take fewer steps than conventional LL(1) grammar. The ranks and asymptotic significance depict that the GNF based LL(1) method is significant than the conventional LL(1) approach. The study adds to the knowledge of parsers itself, parser expression grammars (PEG’s), LL(1) grammars, Greibach Normal Form (GNF) induced grammar structure, and the induction of Arithmetic PEG’s LL(1) to GNF based grammar.

Alternative Vidhi to Conversion of Cyclic CNF->GNF

In automata theory Greibach Normal Form shows that A->aV n*, where ‘a’ is terminal symbol and Vn is nonterminal symbol where * shows zero or more rates of Vn [1]. Most popular questions, conversion of following cyclic CNF into GNF are: Question 1 S->AA | a, A->SS | b Question 2 S->AB, A->BS | b, B->SA | a Question 3 S->AB, A->BS | b, B->AS | a [1] To solve these questions, we need two technical lemmas and required one or more another variable like Z1. In these questions, we have cyclic nature of production called cyclic CNF. We have modified the same rule by which we get the more reliable answer with less number of productions in right hand side without using lemmas and any another variable. This above method can be applied on all problems by which we produce the GNF.

GENERATING ALL CIRCULAR SHIFTS BY CONTEXT-FREE GRAMMARS IN GREIBACH NORMAL FORM

For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates Cn. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals ν(n), the number of rules π(n) and the number of leftmost derivations δ(n) of Gn. As in the case of Chomsky normal form, these ν, π and δ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal w. r. t. all these measures remains open.