I need c and d the second image contains what 7.1.2 asks. The topic is automata theory ### Exercise 7.1.3: Grammar Problems#### Problem Statement:Repeat Exercise 7.1.2 for the following grammar:#### Production Rules:- \( S \rightarrow 0A0 \) | \( 1B1 \) | \( BB \)- \( A \rightarrow C \)- \( B \rightarrow S \) | \( A \)- \( C \rightarrow S \) | \( \epsilon \)In this exercise, you are tasked with analyzing and manipulating the given context-free grammar as specified in Exercise 7.1.2. Make sure to follow the prescribed steps and guidelines for context-free grammar transformations and derivations. ### Steps to Simplify Grammar for Chomsky Normal Form1. **Eliminate ε-productions:** To begin with, remove all the ε-productions (productions that generate the empty string ε) from the grammar. This is essential to simplify the grammar without altering the language it generates.2. **Eliminate Unit Productions:** After removing ε-productions, eliminate unit productions. A unit production is of the form \( A \rightarrow B \), where A and B are non-terminal symbols. Replace these with equivalent productions that directly generate terminal symbols whenever possible.3. **Eliminate Useless Symbols:** Identify and remove any useless symbols in the resulting grammar. Useless symbols are those that do not contribute to generating any string in the language. This process ensures that only the necessary components remain in the grammar.4. **Convert to Chomsky Normal Form (CNF):** Finally, transform the resulting grammar into Chomsky Normal Form. In CNF, every production rule is of the form \( A \rightarrow BC \) or \( A \rightarrow a \), where A, B, and C are non-terminal symbols and a is a terminal symbol. This standard form is beneficial for theoretical analyses and algorithmic implementations.By following these steps, the grammar will be in a simplified, normalized form suitable for further computational processes.

SOLUTION -7.1.3 -Given,S→0A0 | 1B1 | BBA→CB→S | AC→S | ϵ(a)Elimination of ϵ-productions in the…

Answered: Exercise 7.1.3: Repeat Exercise 7.1.2…

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Exercise 7.1.3: Repeat Exercise 7.1.2 for the following grammar: S → 040|11|BB A B C ↑↑↑↑ C S\A Sle

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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Time Complexity

In computer science, the computational complexity that is measured in terms of time is referred to as time complexity that defines how long it takes a computer to execute an algorithm. An algorithm's time complexity is measured by the the amount of time required to execute each statement of code in the algorithm. If a statement is set to execute repetitively, the number of times it will be N multiplied by the time it takes to run that function each time is equal .

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I need c and d the second image contains what 7.1.2 asks. The topic is automata theory

### Exercise 7.1.3: Grammar Problems

#### Problem Statement:
Repeat Exercise 7.1.2 for the following grammar:

#### Production Rules:
- \( S \rightarrow 0A0 \) | \( 1B1 \) | \( BB \)
- \( A \rightarrow C \)
- \( B \rightarrow S \) | \( A \)
- \( C \rightarrow S \) | \( \epsilon \)

In this exercise, you are tasked with analyzing and manipulating the given context-free grammar as specified in Exercise 7.1.2. Make sure to follow the prescribed steps and guidelines for context-free grammar transformations and derivations.

### Steps to Simplify Grammar for Chomsky Normal Form

1. **Eliminate ε-productions:**
To begin with, remove all the ε-productions (productions that generate the empty string ε) from the grammar. This is essential to simplify the grammar without altering the language it generates.

2. **Eliminate Unit Productions:**
After removing ε-productions, eliminate unit productions. A unit production is of the form \( A \rightarrow B \), where A and B are non-terminal symbols. Replace these with equivalent productions that directly generate terminal symbols whenever possible.

3. **Eliminate Useless Symbols:**
Identify and remove any useless symbols in the resulting grammar. Useless symbols are those that do not contribute to generating any string in the language. This process ensures that only the necessary components remain in the grammar.

4. **Convert to Chomsky Normal Form (CNF):**
Finally, transform the resulting grammar into Chomsky Normal Form. In CNF, every production rule is of the form \( A \rightarrow BC \) or \( A \rightarrow a \), where A, B, and C are non-terminal symbols and a is a terminal symbol. This standard form is beneficial for theoretical analyses and algorithmic implementations.

By following these steps, the grammar will be in a simplified, normalized form suitable for further computational processes.

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