**Converting Grammar Rules to Chomsky Normal Form (CNF)**In this lesson, we will focus on converting the given set of grammar rules to Chomsky Normal Form (CNF). CNF is a type of context-free grammar where each rule is of the form:1. \( A \rightarrow BC \) (where \( A \), \( B \), and \( C \) are non-terminal symbols, and \( B \) and \( C \) are not start symbols) 2. \( A \rightarrow a \) (where \( A \) is a non-terminal symbol and \( a \) is a terminal symbol)Given grammar rules:\[ A \rightarrow ABA \ | \ B \ | \ a \ | \ ab \]\[ B \rightarrow BCB \ | \ C \ | \ b \ | \ bc \ | \ \epsilon \]\[ C \rightarrow CD \ | \ DC \ | \ c \]\[ D \rightarrow D \ | \ \epsilon \]Here are the steps involved in converting these rules to CNF:1. **Remove ε-productions**: Get rid of productions that produce an empty string (ε), except when the start symbol itself can generate ε.2. **Remove unit productions**: Productions where one non-terminal goes to another non-terminal.3. **Eliminate useless symbols**: Remove any non-terminal symbols that do not appear in any derivations of terminal strings.4. **Break down long productions**: Ensure that each production has at most two non-terminals on the right-hand side, or a single terminal.### Explanation#### Step 1: Remove ε-productions- From \( B \rightarrow \epsilon \)- From \( D \rightarrow \epsilon \)#### Step 2: Remove unit productionsUnit productions such as \( A \rightarrow B \), \( B \rightarrow C \), etc., need to be replaced with equivalent productions without chaining single non-terminal to another.#### Step 3: Eliminate long Productions- Productions like \(A \rightarrow ABA \), \( BCB \) need to be decomposed to follow CNF rules.Here is the systematic approach to convert it to CNF:#### Intermediate Grammars Post Transformation:1. **Eliminating ε-productions:** We introduce new rules for possibilities without ε. For \( B \rightarrow b \mid C \mid bC \mid b \

Given :- A -> ABA | B | a | ab B -> BCB | C | b | bc | epsilon C -> CD | DC | c D ->…

Answered: onvert these rules to CNF. A → ABA|…

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Computer Science

onvert these rules to CNF. A → ABA| B|a|ab B→BCB|C|b|bc|e C→CD|DC|c D→D E

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Convert this PDA to CFG The language is L = {anbm : m >= n, where m-n is even}
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Subject: Theory of Automata
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