1
GATE CSE 2014 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let $${L_1} = \left\{ {w \in \left\{ {0,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(110)'s$$ as $$(011)'s$$$$\left. \, \right\}$$. Let $${L_2} = \left\{ {w \in \left\{ {0,\,\,1} \right\}{}^ * \left| w \right.} \right.$$ has at least as many occurrences of $$(000)'s$$ as $$(111)'s$$$$\left. \, \right\}$$. Which one of the following is TRUE?
A
$${L_1}$$ is regular but not $${L_2}$$
B
$${L_2}$$ is regular but not $${L_1}$$
C
Both $${L_1}$$ and $${L_2}$$ are regular
D
Neither $${L_1}$$ nor $${L_2}$$ are regular
2
GATE CSE 2013
MCQ (Single Correct Answer)
+2
-0.6
Consider the following languages
$${L_1} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{0^p}{1^q}{0^r}\left| {p,q,r \ge 0,p \ne r} \right.} \right\}$$

Which one of the following statements is FALSE?

A
$${L_2}$$ is context-free
B
$${L_1} \cap {L_2}$$ is context-free
C
Complement of $${L_2}$$ is recursive
D
Complement of $${L_1}$$ is context-free but not regular
3
GATE CSE 2012
MCQ (Single Correct Answer)
+2
-0.6
Consider the set of strings on $$\left\{ {0,1} \right\}$$ in which, every substring of $$3$$ symbols has at most two zeros. For example, $$001110$$ and $$011001$$ are in the language, but $$100010$$ is not. All strings of length less than $$3$$ are also in the language. A partially completed $$DFA$$ that accepts this language is shown below.

The missing arcs in the $$DFA$$ are

GATE CSE 2012 Theory of Computation - Finite Automata and Regular Language Question 41 English
A
GATE CSE 2012 Theory of Computation - Finite Automata and Regular Language Question 41 English Option 1
B
GATE CSE 2012 Theory of Computation - Finite Automata and Regular Language Question 41 English Option 2
C
GATE CSE 2012 Theory of Computation - Finite Automata and Regular Language Question 41 English Option 3
D
GATE CSE 2012 Theory of Computation - Finite Automata and Regular Language Question 41 English Option 4
4
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
Definition of the language $$L$$ with alphabet $$\left\{ a \right\}$$ is given as following. $$L = \left\{ {{a^{nk}}} \right.\left| {k > 0,\,n} \right.$$ is a positive integer constant$$\left. \, \right\}$$

What is the minimum number of states needed in a $$DFA$$ to recognize $$L$$?

A
$$k+1$$
B
$$n+1$$
C
$${2^{n + 1}}$$
D
$${2^{k + 1}}$$
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12