Regular Language


Q1.

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?
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Q2.

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?
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Q3.

For \Sigma =\{a,b\}, let us consider the regular language L=\{x|x=a^{2+3k} \; or \; x=b^{10+12k}, k\geq 0\}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?
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Q4.

If L is a regular language over \Sigma =\{a,b\}, which one of the following languages is NOT regular ?
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Q5.

Let L \subseteq \Sigma^* where \Sigma = \left\{a,b \right\}. Which of the following is true?
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Q6.

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?
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Q7.

Consider the following two statements about regular languages: S1: Every infinite regular language contains an undecidable language as a subset. S2: Every finite language is regular. Which one of the following choices is correct?
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Q8.

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\}
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Q9.

Which of the following are regular sets? I. \{a^{n}b^{2m}|n\geq 0,m\geq 0\} II. \{a^{n}b^{m}|n=2m\} III. \{a^{n}b^{m}|n\neq m\} IV. \{xcy|x,y,\in \{a,b\}^*\}
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Q10.

Which of the following statements is false?
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