October 13, 2023
October 13, 2023
October 13, 2023
###### UGC NET CS 2007 June-Paper-2
October 13, 2023
 Question 5
Which of the following language is regular :
 A L = { an bn| n ≥ 1 } B L = { an bm cn dm|n, m ≥ 1 } C L = { an bm|n, m ≥ 1 } D L = { an bm cn|n, m ≥ 1 }
Question 5 Explanation:
Language generated in Option (A) requires a memory element to count an equal number of b’s after a. And since regular languages are accepted by finite automata which do not have a memory element. Hence Option (A) language is not Regular.

Language generated in Option (B) requires a memory element and a read-write head which can move in both directions to count equal numbers of a’s and c’s , and b’s and d’s. And since regular languages are accepted by finite automata which do not have a memory element and a read-write head which can move in both directions. Hence Option (A) language is not Regular.

Language generated in Option (C) is regular because the number of a’s and b’s does not necessarily need to be the same which means no memory element is required. Hence it is a regular language.

Language generated in Option (D) requires a memory element to count an equal number of c’s after a. And since regular languages are accepted by finite automata which do not have a memory element. Hence Option (A) language is not Regular. The language generated here is context free language which can be accepted by pushdown automata.

Question 5 Explanation:
Language generated in Option (A) requires a memory element to count an equal number of b’s after a. And since regular languages are accepted by finite automata which do not have a memory element. Hence Option (A) language is not Regular.

Language generated in Option (B) requires a memory element and a read-write head which can move in both directions to count equal numbers of a’s and c’s , and b’s and d’s. And since regular languages are accepted by finite automata which do not have a memory element and a read-write head which can move in both directions. Hence Option (A) language is not Regular.

Language generated in Option (C) is regular because the number of a’s and b’s does not necessarily need to be the same which means no memory element is required. Hence it is a regular language.

Language generated in Option (D) requires a memory element to count an equal number of c’s after a. And since regular languages are accepted by finite automata which do not have a memory element. Hence Option (A) language is not Regular. The language generated here is context free language which can be accepted by pushdown automata.