Conjunctive Grammars in Greibach Normal Form and the Lambek Calculus with Additive Connectives

An overview is given of cover results for normal forms of regular grammars. Due to the special form of regular grammars and due to the results which are obtained it is sufficient to consider covering grammars in Greibach normal form. Among other things it is proved that any left-regular grammar can be left covered with a context-free grammar in Greibach normal form. All the cover results concerning the left- and right-regular grammars are listed, with respect to several types of covers, in a cover table.

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

Quaid-e-Awam University Research Journal of Engineering, Science & Technology ◽

10.52584/qrj.1802.14 ◽

2020 ◽

Vol 18 (02) ◽

pp. 89-101

Author(s):

Hassan Ali ◽

Muhammad Shumail Naveed ◽

Dilawar Naseem ◽

Jawaid Shabbir

Keyword(s):

Statistical Analysis ◽

Normal Form ◽

Processing Speed ◽

Statistical Significance ◽

Transformation Method ◽

Arithmetic Expression ◽

Kolmogorov Smirnov ◽

Prime Objective ◽

Greibach Normal Form ◽

Arithmetic Expressions

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.

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Greibach normal form transformation, revisited

Lecture Notes in Computer Science - STACS 97 ◽

10.1007/bfb0023447 ◽

1997 ◽

pp. 47-54 ◽

Cited By ~ 5

Author(s):

Robert Koch ◽

Norbert Blum

Keyword(s):

Normal Form ◽

Form Transformation ◽

Normal Form Transformation ◽

Greibach Normal Form

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Alternative Vidhi to Conversion of Cyclic CNF->GNF

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY ◽

10.24297/ijct.v3i1b.6778 ◽

2012 ◽

Vol 3 (1) ◽

pp. 132-133

Author(s):

Avinash Bansal

Keyword(s):

Normal Form ◽

Automata Theory ◽

Terminal Symbol ◽

Nonterminal Symbol ◽

Right Hand ◽

Greibach Normal Form

In automata theory Greibach Normal Form shows that A->aV n*, where â€˜aâ€™ 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.

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