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WHICH OF THE FOLLOWING LANGUAGES IS ACCEPTED BY A DETERMINISTIC PUSHDOWN AUTOMATA (DPDA)?

  1. $L_1=\left\{a^n b^n c^k \mid n, k \geq 0\right\} \cup\left\{a^i b^j c^j \mid i, j \geq 0\right\}$
     
  2. $L_2=\left\{a^n b^m c^n d^m \mid n, m \geq 0\right\}$
     
  3. $L_3=\left\{a^n b^n \mid n \geq 0\right\} \cup\left\{a^n b^{2 n} \mid n \geq 0\right\}$
     
  4. $L_4=\left\{a^n b^n c^k d^k \mid n, k \geq 0\right\}$

3 Answers

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This shows DPDA is not closed under Union.
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