**Problem Statement:**Given the language \[ L = \{(ba)^m, a^mb^n, aa : m, n \geq 0\} \]find the regular expression \( r \) such that \( L(r) = L \).**Explanation:**The language \( L \) consists of three different types of strings:1. Strings of the form \((ba)^m\), where \( m \) is a non-negative integer (i.e., the string "ba" repeated \( m \) times).2. Strings of the form \( a^m b^n \), where \( m \) and \( n \) are non-negative integers (i.e., \( m \) consecutive 'a's followed by \( n \) consecutive 'b's).3. The fixed string "aa".The task is to find a regular expression that encompasses all these possibilities such that any string generated by this expression belongs to the language \( L \).

Answered: OGiven the language L = {(ba)™, a™b",…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

**Problem Statement:**

Given the language

\[ L = \{(ba)^m, a^mb^n, aa : m, n \geq 0\} \]

find the regular expression \( r \) such that \( L(r) = L \).

**Explanation:**

The language \( L \) consists of three different types of strings:

1. Strings of the form \((ba)^m\), where \( m \) is a non-negative integer (i.e., the string "ba" repeated \( m \) times).
2. Strings of the form \( a^m b^n \), where \( m \) and \( n \) are non-negative integers (i.e., \( m \) consecutive 'a's followed by \( n \) consecutive 'b's).
3. The fixed string "aa".

The task is to find a regular expression that encompasses all these possibilities such that any string generated by this expression belongs to the language \( L \).

Expert Solution

Step 1

regular expression:The language accepted by finite automata can be easily described by simple expressions called Regular Expressions. It is the most effective way to represent any language.The languages accepted by some regular expression are referred to as Regular languages.A regular expression can also be described as a sequence of pattern that defines a string.Regular expressions are used to match character combinations in strings. String searching algorithm used this pattern to find the operations on a string.