Question:
The language \(L=\{0^n1^n2^n\mid n\ge0\}\) is a
The language \(L=\{0^n1^n2^n\mid n\ge0\}\) is a
Show Hint
\[
\{a^n b^n\}
\]
is Context-Free, while
\[
\{a^n b^n c^n\}
\]
is Context-Sensitive.
Updated On: Jun 25, 2026
- Context free language
- Regular language
- Context sensitive language
- Recursively enumerable language
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The Correct Option is C
Solution and Explanation
Concept:
The language
\[
\{0^n1^n2^n\}
\]
requires simultaneous counting of three symbol groups.
Step 1: Check regularity.
The language is not regular because equal counts must be maintained.
Step 2: Check context-freeness.
A PDA can compare only two groups conveniently using a stack. The language \[ 0^n1^n2^n \] is not context free.
Step 3: Classify the language.
It is a standard example of a context-sensitive language. \[ \boxed{L \in CSL} \]
Step 1: Check regularity.
The language is not regular because equal counts must be maintained.
Step 2: Check context-freeness.
A PDA can compare only two groups conveniently using a stack. The language \[ 0^n1^n2^n \] is not context free.
Step 3: Classify the language.
It is a standard example of a context-sensitive language. \[ \boxed{L \in CSL} \]
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