List of top Theory of Computation Questions on Context Free Languages asked in GATE CS

Let \(\Sigma = \{a, b, c, d\}\) and let \(L = \{a^i b^j c^k d^l \mid i, j, k, l \geq 0\}\). Which of the following constraints ensure(s) that the language \(L\) is context-free?

Consider the following two languages over the alphabet \( \{a, b, c\} \), where \( m \) and \( n \) are natural numbers. \[ L_1 = \{ a^m b^{m+n} c^{m+n} \mid m, n \geq 1 \} \] \[ L_2 = \{ a^m b^n c^{m+n} \mid m, n \geq 1 \} \] Which ONE of the following statements is CORRECT?