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
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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.
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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