Question:
Which among the following cannot be accepted by a regular grammar?
Which among the following cannot be accepted by a regular grammar?
Show Hint
The language
\[
\{a^n b^n\}
\]
is the most famous example of a non-regular language.
Updated On: Jun 25, 2026
- L is a set of numbers divisible by 2
- L is a set of binary complement
- L is a set of string with odd number of 0
- L is a set of \(0^n1^n\)
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The Correct Option is D
Solution and Explanation
Concept:
Regular grammars generate exactly the regular languages.
A language is regular if it can be accepted by a finite automaton.
Step 1: Analyze each language.
Numbers divisible by 2, binary complement patterns, and strings containing odd numbers of \(0\)'s can all be recognized using finite automata. Hence they are regular languages.
Step 2: Consider \(0^n1^n\).
\[ L=\{0^n1^n\mid n\ge0\} \] requires matching equal numbers of \(0\)'s and \(1\)'s. A finite automaton has no memory to count arbitrarily large values of \(n\). Hence this language is not regular.
Step 3: Write the answer.
Therefore, \[ \boxed{0^n1^n} \] cannot be generated by a regular grammar.
Step 1: Analyze each language.
Numbers divisible by 2, binary complement patterns, and strings containing odd numbers of \(0\)'s can all be recognized using finite automata. Hence they are regular languages.
Step 2: Consider \(0^n1^n\).
\[ L=\{0^n1^n\mid n\ge0\} \] requires matching equal numbers of \(0\)'s and \(1\)'s. A finite automaton has no memory to count arbitrarily large values of \(n\). Hence this language is not regular.
Step 3: Write the answer.
Therefore, \[ \boxed{0^n1^n} \] cannot be generated by a regular grammar.
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