Which of the following are not regular ? (A) Strings of even number of a’s. (B) Strings of a’s, whose length is a prime number. (C) Set of all palindromes made up of a’s and b’s. (D) Strings of a’s whose length is a perfect square.
(B), (C) and (D) only
A language is regular when a finite automaton can accept it; the pumping lemma shows non-regularity when pumping a substring pushes a string out of the language.
(A) Even number of a’s is \((aa)^*\), accepted by a two-state DFA — regular.
(B) \(\{a^p : p \text{ prime}\}\): pumping \(a^p\) with a block of length k gives lengths p + ik; choosing i = p gives p(1 + k), which is composite — not regular.
(C) Palindromes over {a, b}: pumping the leading a’s of \(a^n b a^n\) breaks the symmetry — not regular (it needs a stack).
(D) \(\{a^{m^2}\}\): consecutive squares differ by 2m + 1, which grows without bound, while pumping adds a fixed amount ≤ n, landing strictly between \(n^2\) and \((n+1)^2\) — not regular.
So exactly (B), (C) and (D) are not regular. Any choice that includes (A) wrongly calls a regular language non-regular, and (B) and (D) alone misses the palindromes.
(B), (C) and (D) only option is correct.
Similar Questions
Regular expression for the complement of language \(L = \{a^n b^m \mid n \ge 4,\ m \le 3\}\) is
Given two languages :
\(L_1 = \{(ab)^n a^k \mid n \gt k,\ k \ge 0\}\)
\(L_2 = \{a^n b^m \mid n \ne m\}\)
Using pumping lemma for regular language, it can be shown that
Which of the following statements is false ?
The regular expression corresponding to the language L where
\(L = \{ x \in \{0, 1\}^{*} \mid x\) ends with 1 and does not contain substring 00 \(\}\) is :
Let L be any language. Define even (W) as the strings obtained by extracting from W the letters in the even-numbered positions and even(L) = {even (W) | W ∈ L}. We define another language Chop (L) by removing the two leftmost symbols of every string in L given by \(\text{Chop}(L) = \{W \mid \nu W \in L, \text{ with } |\nu| = 2\}\).
If L is regular language then
For the above specified passage, which of the following represents the regular expression?
Which of the following properties correctly describe a Regular Grammar ?
(A) All production rules are of the form A→xB or A→x, where A and B are non terminal symbols and x is a terminal symbol.
(B) Regular grammars are more powerful than context-free grammars and can express any type of language.
(C) There is a direct correspondence between regular grammar and finite automata.
(D) Regular grammars can generate languages that are not recognised by any type of automata.
Choose the correct answer from the options given below :
The precedence of regular expression operators from lowest to highest precedence is:
Which of the following is TRUE about the Pumping Lemma for regular language?
Consider the following two languages :
L1 = {0i1j| gcd (i, j) = 1}
L2 is any subset of 0*.
Which of the following is correct ?
Important Questions from Regular Languages
Which of the following are correct on regular expressions?
A. φ + L = L + φ = L
B. εL = Lε = L
C. φL = Lφ = φ
D. φL = Lφ = L
Choose the correct answer from the options given below:
- Let $L_1$ and $L_2$ be two languages over a finite alphabet, such that $L_1 \cap L_2$ and $L_2$ are regular languages.
Which of the following statements is/are always true? Regular expression for the complement of language \(L = \{a^n b^m \mid n \ge 4,\ m \le 3\}\) is
Given two languages :
\(L_1 = \{(ab)^n a^k \mid n \gt k,\ k \ge 0\}\)
\(L_2 = \{a^n b^m \mid n \ne m\}\)
Using pumping lemma for regular language, it can be shown that
- Let $\Sigma = \{a, b, c\}$. For $x \in \Sigma^*$, and $a \in \Sigma$, let $\#_a(x)$ denote the number of occurrences of $a$ in $x$.
Which one or more of the following option(s) define(s) regular language(s)?
