Theory of Computation
Q161.
Let L be a regular language. Consider the constructions on L below: I. \text{repeat} (L) = \{ww \mid w \in L\} II. \text{prefix} (L) = \{u \mid \exists v : uv \in L\} III. \text{suffix} (L) = \{v \mid \exists u: uv \in L\} IV. \text{half} (L) = \{u \mid \exists v: | v | = | u | \text{ and } uv \in L\} Which choice of L is best suited to support your answer above?Q162.
Which of the following languages is/are regular? L_{1}:\{wxw^{R}|w,x \in \{a,b\}^{*} \; and \; |w|,|x| \gt 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\}Q164.
Let P be a regular language and Q be a context free language such that Q \subseteq P. (For example, let P be the language represented by the regular expression p*q* and Q be \{p^{n}q^{n}|n\in N\} Then which of the following is ALWAYS regular?Q165.
Let L \subseteq \{0,1\}^* be an arbitrary regular language accepted by a minimal DFA with k states. Which one of the following languages must necessarily be accepted by a minimal DFA with k states?Q166.
Let L \subseteq \Sigma^* where \Sigma = \left\{a,b \right\}. Which of the following is true?Q167.
If L_{1}=\{a^{n}|n\geq 0\} and L_{2}=\{b^{n}|n\geq 0 \}, Consider (I) L_{1}\cdot L_{2} is a regular language (II) L_{1} \cdot L_{2}= \{a^{n}b^{n}|n \geq 0\} Which one of the following is CORRECT?Q169.
Consider the following statements. I. If L_1\cup L_2 is regular, then both L_1 \; and \; L_2 must be regular. II. The class of regular languages is closed under infinite union. Which of the above statements is/are TRUE?