Which of the following languages is/are regular? {\L}_1: \{{wxw^{R }} ∣ {\w}, {\x} \epsilon\{ {\a}, {\b}\}^*. and |w|,|x|>0\} , {\w}^{ {\R}} is the reverse of string {\w} {\L}_2: \{ {\a}^{ {\n}} {\b}^{ {\m}} ∣ {\m} \neq {\n}. and m, {\n} \geq 0\} L_3: \{a^p b^q c^r ∣ p, q, r \geq 0\}

Correct Answer is : L1 and L3 only

GATE Computer Science (CS) 2015 Shift 2 Solved Paper

Question : 46 of 65

Marks: +1, -0

Which of the following languages is/are regular?

{\L}_1: \{{wxw^{R }} ∣ {\w}, {\x} ε\{ {\a}, {\b}\}^*.

and

|w|,|x|>0\} , {\w}^{ {\R}}

is the reverse of string

{\w}

{\L}_2: \{ {\a}^{ {\n}} {\b}^{ {\m}} ∣ {\m} ≠ {\n}.

and

m, {\n} ≥ 0\}

L_3: \{a^p b^q c^r ∣ p, q, r ≥ 0\}

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