**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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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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Question

**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 productions

Unit 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 \

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