1
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+2
-0.67

Consider the following language.

L = { w ∈ {0, 1}* | w ends with the substring 011}

Which one of the following deterministic finite automata accepts L?

A
GATE CSE 2021 Set 1 Theory of Computation - Finite Automata and Regular Language Question 18 English Option 1
B
GATE CSE 2021 Set 1 Theory of Computation - Finite Automata and Regular Language Question 18 English Option 2
C
GATE CSE 2021 Set 1 Theory of Computation - Finite Automata and Regular Language Question 18 English Option 3
D
GATE CSE 2021 Set 1 Theory of Computation - Finite Automata and Regular Language Question 18 English Option 4
2
GATE CSE 2020
Numerical
+2
-0
Consider the following language.

L = {x $$ \in $$ {a, b}* | number of a’s in x is divisible by 2 but not divisible by 3}

The minimum number of states in a DFA that accepts L is ______.
Your input ____
3
GATE CSE 2019
Numerical
+2
-0
Let $\Sigma$ be the set of all bijections from $\{1, \ldots, 5\}$ to $\{1, \ldots, 5\}$, where id denotes the identity function, i.e. $\operatorname{id}(j)=j, \forall j$. Let $\circ$ denote composition on functions. For a string $x=$ $x_1 x_2 \cdots x_n \in \Sigma^n, n \geq 0$, let $\pi(x)=x_1 \circ x_2 \circ \cdots \circ x_n$. Consider the language $L=\left\{x \in \Sigma^* \mid \pi(x)=i d\right\}$. The minimum number of states in any DFA accepting $L$ is $\qquad$
Your input ____
4
GATE CSE 2018
Numerical
+2
-0
Given a language $$𝐿,$$ define $${L^i}$$ as follows: $${L^0} = \left\{ \varepsilon \right\}$$
$${L^i} = {L^{i - 1}}.\,\,L$$ for all $$i > 0$$

The order of a language $$L$$ is defined as the smallest k such that $${L^k} = {L^{k + 1}}.$$ Consider the language $${L_1}$$ (over alphabet $$0$$) accepted by the following automaton.

GATE CSE 2018 Theory of Computation - Finite Automata and Regular Language Question 24 English

The order of $${L_1}$$ is _____.

Your input ____
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