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Module 2: Context-free languages and pushdown automata

20192m

Consider the following languages:
GATE[2005]
L1={wwRw{0,1}}L_1 = \{ww^R \mid w \in \{0, 1\}^*\}
L2={w#wRw{0,1}}L_2 = \{w\#w^R \mid w \in \{0, 1\}^*\}
where #\# is a special symbol,
L3={www{0,1}}L_3 = \{ww \mid w \in \{0, 1\}^*\}

Which one of the following is true?
(i) L1L_1 is a deterministic CFL
(ii) L2L_2 is a deterministic CFL
(iii) L3L_3 is a CFL, but not a deterministic CFL
(iv) L3L_3 is a deterministic CFL

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