1
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 $$i > 0$$
$${L^i} = {L^{i - 1}}.\,\,L$$ 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 18 English](https://gateclass.static.cdn.examgoal.net/BmaaYEPG0RHbPqsWW/c32wm37WqR4o8DmlYw9WaAd1HijtO/QpeWSftexyaCIK0WyXS76J/uploadfile.jpg)
The order of $${L_1}$$ is _____.
Your input ____
2
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider the following two statements:
$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$ If all states of an $$NFA$$ are accepting states then the language accepted by the
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$NFA$$ is $$\sum {^ * } .$$
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,$$ There exists a regular language $$A$$ such that for all languages $$B,A \cap B$$ is
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ regular.
Which one of the following is CORRECT?
3
GATE CSE 2016 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Consider the following languages:
$$$\eqalign{
& {L_1} = \left\{ {{a^n}{b^m}{c^{n + m}}:m,n \ge 1} \right\} \cr
& {L_2} = \left\{ {{a^n}{b^n}{c^{2n}}:n \ge 1} \right\} \cr} $$$
Which one of the following is TRUE?
4
GATE CSE 2016 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Consider the transition diagram of a $$PDA$$ given below with input alphabet $$\sum {\, = \left\{ {a,b} \right\}} $$ and stack alphabet $$\Gamma = \left\{ {X,Z} \right\}.$$ $$Z$$ is the initial stack symbol. Let $$L$$ denote the language accepted by the $$PDA.$$
![GATE CSE 2016 Set 1 Theory of Computation - Finite Automata and Regular Language Question 24 English](https://gateclass.cdn.examgoal.net/Hdz2WTN4RD2stL3xx/v1kerT30NJEPhyx1OX1DfVoDO1pir/jVXoiWgIRPd356qJzNlkux/uploadfile.jpg)
Which one of the following is TRUE?
Questions Asked from Finite Automata and Regular Language (Marks 2)
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