Let language L over alphabet Σ = { a, b } be defined as L = { a'b* }, where i is a multiple of some given n and k is a multiple of some given m, all non- negative integers. In other words: L contains all strings consisting of: o A number of a's that is a multiple of n o followed by a number of b's that is a multiple of m. Using a constructive method, show that for any given values of n and m, L is regular.
Let language L over alphabet Σ = { a, b } be defined as L = { a'b* }, where i is a multiple of some given n and k is a multiple of some given m, all non- negative integers. In other words: L contains all strings consisting of: o A number of a's that is a multiple of n o followed by a number of b's that is a multiple of m. Using a constructive method, show that for any given values of n and m, L is regular.
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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![### Language Definition and Regularity Proof
#### Language L Definition:
Let language \( L \) over alphabet \( \Sigma = \{ a, b \} \) be defined as
\[ L = \{ a^i b^k \} \]
where \( i \) is a multiple of some given \( n \) and \( k \) is a multiple of some given \( m \), all non-negative integers.
In other words:
\( L \) contains all strings consisting of:
- A number of \( a \)'s that is a multiple of \( n \)
- Followed by a number of \( b \)'s that is a multiple of \( m \)
#### Constructive Method for Regularity:
Using a constructive method, show that for any given values of \( n \) and \( m \), \( L \) is regular.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02653cd8-bf86-4163-910a-cf0838bd0b6e%2Fdd3d320a-0d4a-4d72-ade2-33ab60f6c792%2F3i4ltvk_processed.png&w=3840&q=75)
Transcribed Image Text:### Language Definition and Regularity Proof
#### Language L Definition:
Let language \( L \) over alphabet \( \Sigma = \{ a, b \} \) be defined as
\[ L = \{ a^i b^k \} \]
where \( i \) is a multiple of some given \( n \) and \( k \) is a multiple of some given \( m \), all non-negative integers.
In other words:
\( L \) contains all strings consisting of:
- A number of \( a \)'s that is a multiple of \( n \)
- Followed by a number of \( b \)'s that is a multiple of \( m \)
#### Constructive Method for Regularity:
Using a constructive method, show that for any given values of \( n \) and \( m \), \( L \) is regular.
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