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Recent questions tagged regular-languages
0
votes
2
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1
UGCNET-Oct2020-II: 56
Consider the following languages: $L_1=\{a^{\grave{z}^z} \mid \grave{Z} \text{ is an integer} \}$ $L_2=\{a^{z\grave{z}} \mid \grave{Z} \geq 0\}$ $L_3=\{ \omega \omega \mid \omega \epsilon \{a,b\}^*\}$ Which of the languages is(are) regular? Choose the correct answer from the options given below: $L_1$ and $L_2$ only $L_1$ and $L_3$ only $L_1$ only $L_2$ only
Consider the following languages: $L_1=\{a^{\grave{z}^z} \mid \grave{Z} \text{ is an integer} \}$ $L_2=\{a^{z\grave{z}} \mid \grave{Z} \geq 0\}$ $L_3=\{ \omega \omega \mid \omega \epsilon \{a,b\}^*\}$ Which of the languages is(are) regular? Choose the correct answer from the options given below: $L_1$ and $L_2$ only $L_1$ and $L_3$ only $L_1$ only $L_2$ only
asked
Nov 20, 2020
in
Theory of Computation
jothee
83
views
ugcnet-oct2020-ii
theory-of-computation
regular-languages
1
vote
3
answers
2
NIELIT 2017 DEC Scientific Assistant A - Section B: 15
If $L1$ and $L2$ are regular sets then intersection of these two will be : Regular Non Regular Recursive Non Recursive
If $L1$ and $L2$ are regular sets then intersection of these two will be : Regular Non Regular Recursive Non Recursive
asked
Mar 31, 2020
in
Theory of Computation
Lakshman Patel RJIT
223
views
nielit2017dec-assistanta
theory-of-computation
regular-languages
2
votes
5
answers
3
NIELIT 2016 MAR Scientist B - Section C: 27
If $L$ be a language recognizable by a finite automaton, then language from $\{L\} = \{w$ such that $w$ is a prefix of $v$ where $v\in L\}$, is a regular language. context-free language. context-sensitive language. recursive enumeration language
If $L$ be a language recognizable by a finite automaton, then language from $\{L\} = \{w$ such that $w$ is a prefix of $v$ where $v\in L\}$, is a regular language. context-free language. context-sensitive language. recursive enumeration language
asked
Mar 31, 2020
in
Theory of Computation
Lakshman Patel RJIT
300
views
nielit2016mar-scientistb
theory-of-computation
regular-languages
0
votes
4
answers
4
NIELIT 2016 MAR Scientist B - Section C: 28
Which of the following statements is correct? $A=\{a^nb^n\mid n= 0,1,2,3\dots \}$ is regular language Set $B$ of all strings of equal number of $a$'s and $b$'s defines a regular language $L(A^*B^*) \cap B$ gives the set $A$ None of these.
Which of the following statements is correct? $A=\{a^nb^n\mid n= 0,1,2,3\dots \}$ is regular language Set $B$ of all strings of equal number of $a$'s and $b$'s defines a regular language $L(A^*B^*) \cap B$ gives the set $A$ None of these.
asked
Mar 31, 2020
in
Theory of Computation
Lakshman Patel RJIT
240
views
nielit2016mar-scientistb
theory-of-computation
regular-languages
0
votes
2
answers
5
UGCNET-Jan2017-III: 19
Which of the following are not regular? Strings of even number of a’s Strings of a’s , whose length is a prime number. Set of all palindromes made up of a’s and b’s. Strings of a’s whose length is a perfect square. (a) and (b) only (a), (b) and (c) only (b),(c) and (d) only (b) and (d) only
Which of the following are not regular? Strings of even number of a’s Strings of a’s , whose length is a prime number. Set of all palindromes made up of a’s and b’s. Strings of a’s whose length is a perfect square. (a) and (b) only (a), (b) and (c) only (b),(c) and (d) only (b) and (d) only
asked
Mar 24, 2020
in
Theory of Computation
jothee
219
views
ugcnetjan2017iii
theory-of-computation
regular-languages
1
vote
3
answers
6
UGCNET-Jan2017-III: 20
Consider the languages $L_{1}= \phi$ and $L_{2}=\{1\}$. Which one of the following represents $L_{1}^{\ast}\cup L_{2}^{\ast} L_{1}^{\ast}$? $\{\in \}$ $\{\in,1\}$ $\phi$ $1^{\ast}$
Consider the languages $L_{1}= \phi$ and $L_{2}=\{1\}$. Which one of the following represents $L_{1}^{\ast}\cup L_{2}^{\ast} L_{1}^{\ast}$? $\{\in \}$ $\{\in,1\}$ $\phi$ $1^{\ast}$
asked
Mar 24, 2020
in
Theory of Computation
jothee
199
views
ugcnetjan2017iii
theory-of-computation
regular-languages
1
vote
3
answers
7
UGCNET-Jan2017-III: 21
Given the following statements: A class of languages that is closed under union and complementation has to be closed under intersection A class of languages that is closed under union and intersection has to be closed under complementation Which of the following options is correct? Both (a) and ... Both (a) and (b) are true (a) is true, (b) is false (a) is false, (b) is true
Given the following statements: A class of languages that is closed under union and complementation has to be closed under intersection A class of languages that is closed under union and intersection has to be closed under complementation Which of the following options is correct? Both (a) and (b) are false Both (a) and (b) are true (a) is true, (b) is false (a) is false, (b) is true
asked
Mar 24, 2020
in
Theory of Computation
jothee
200
views
ugcnetjan2017iii
theory-of-computation
regular-languages
2
votes
3
answers
8
ISRO2020-38
Which of the following is true? Every subset of a regular set is regular Every finite subset of non-regular set is regular The union of two non regular set is not regular Infinite union of finite set is regular
Which of the following is true? Every subset of a regular set is regular Every finite subset of non-regular set is regular The union of two non regular set is not regular Infinite union of finite set is regular
asked
Jan 13, 2020
in
Theory of Computation
Satbir
413
views
isro-2020
theory-of-computation
regular-languages
easy
0
votes
0
answers
9
Michael Sipser Edition 3 Exercise 5 Question 4 (Page No. 239)
If $A \leq_{m} B$ and $B$ is a regular language, does that imply that $A$ is a regular language? Why or why not?
If $A \leq_{m} B$ and $B$ is a regular language, does that imply that $A$ is a regular language? Why or why not?
asked
Oct 19, 2019
in
Theory of Computation
Lakshman Patel RJIT
34
views
michael-sipser
theory-of-computation
regular-languages
reduction
proof
0
votes
0
answers
10
Michael Sipser Edition 3 Exercise 2 Question 44 (Page No. 158)
If $A$ and $B$ are languages, define $A \diamond B = \{xy \mid x \in A\: \text{and}\: y \in B \;\text{and} \mid x \mid = \mid y \mid \}$. Show that if $A$ and $B$ are regular languages, then $A \diamond B$ is a CFL.
If $A$ and $B$ are languages, define $A \diamond B = \{xy \mid x \in A\: \text{and}\: y \in B \;\text{and} \mid x \mid = \mid y \mid \}$. Show that if $A$ and $B$ are regular languages, then $A \diamond B$ is a CFL.
asked
Oct 12, 2019
in
Theory of Computation
Lakshman Patel RJIT
36
views
michael-sipser
theory-of-computation
regular-languages
proof
1
vote
1
answer
11
CMI2019-A-1
Let $L_{1}:=\{a^{n}b^{m}\mid m,n\geq 0\: \text{and}\: m\geq n\}$ and $L_{2}:=\{a^{n}b^{m}\mid m,n\geq 0\: \text{and}\: m < n\}.$ The language $L_{1}\cup L_{2}$ is: regular, but not context-free context-free, but not regular both regular and context-free neither regular nor context-free
Let $L_{1}:=\{a^{n}b^{m}\mid m,n\geq 0\: \text{and}\: m\geq n\}$ and $L_{2}:=\{a^{n}b^{m}\mid m,n\geq 0\: \text{and}\: m < n\}.$ The language $L_{1}\cup L_{2}$ is: regular, but not context-free context-free, but not regular both regular and context-free neither regular nor context-free
asked
Sep 13, 2019
in
Theory of Computation
gatecse
273
views
cmi2019
regular-languages
context-free-languages
closure-property
0
votes
2
answers
12
CMI2019-B-1
Consider an alphabet $\Sigma=\{a,b\}.$ Let $L_{1}$ be the language given by the regular expression $(a+b)^{\ast}bb(a+b)^{\ast}$ and let $L_{2}$ be the language $baa^{\ast}b.$ Define $L:=\{u\in\Sigma^{\ast}\mid \exists w\in L_{2}\: s.t.\: uw\in L_{1}\}.$ Give an example of a word in $L.$ Give an example of a word not in $L.$ Construct an NFA for $L.$
Consider an alphabet $\Sigma=\{a,b\}.$ Let $L_{1}$ be the language given by the regular expression $(a+b)^{\ast}bb(a+b)^{\ast}$ and let $L_{2}$ be the language $baa^{\ast}b.$ Define $L:=\{u\in\Sigma^{\ast}\mid \exists w\in L_{2}\: s.t.\: uw\in L_{1}\}.$ Give an example of a word in $L.$ Give an example of a word not in $L.$ Construct an NFA for $L.$
asked
Sep 13, 2019
in
Theory of Computation
gatecse
324
views
cmi2019
regular-expressions
regular-languages
nfa-dfa
2
votes
3
answers
13
CMI2018-A-1
Which of the words below matches the regular expression $a(a+b)^{\ast}b+b(a+b)^{\ast}a$? $aba$ $bab$ $abba$ $aabb$
Which of the words below matches the regular expression $a(a+b)^{\ast}b+b(a+b)^{\ast}a$? $aba$ $bab$ $abba$ $aabb$
asked
Sep 13, 2019
in
Theory of Computation
gatecse
438
views
cmi2018
regular-languages
regular-expressions
easy
0
votes
0
answers
14
Ullman (TOC) Edition 3 Exercise 9.5 Question 2 (Page No. 418)
Show that the language $\overline{L_A}\cup \overline{L_B}$ is a regular language if and only if it is the set of all strings over its alphabet;i.e., if and only if the instance $(A,B)$ of PCP has no ... homomorphism, complementation and the pumping lemma for regular sets to show that $\overline{L_A}\cup \overline{L_B}$ is not regular.
Show that the language $\overline{L_A}\cup \overline{L_B}$ is a regular language if and only if it is the set of all strings over its alphabet;i.e., if and only if the instance $(A,B)$ of PCP has no solution. Thus, prove that it is ... closed under inverse homomorphism, complementation and the pumping lemma for regular sets to show that $\overline{L_A}\cup \overline{L_B}$ is not regular.
asked
Jul 26, 2019
in
Theory of Computation
Lakshman Patel RJIT
95
views
ullman
theory-of-computation
regular-languages
pcp
descriptive
4
votes
3
answers
15
MadeEasy Test Series: Theory Of Computation - Regular Languages
Consider the following statements: $S_1:\{(a^n)^m|n\leq m\geq0\}$ $S_2:\{a^nb^n|n\geq 1\} \cup \{a^nb^m|n \geq1,m \geq 1\} $ Which of the following is regular? $S_1$ only $S_2$ only Both Neither of the above
Consider the following statements: $S_1:\{(a^n)^m|n\leq m\geq0\}$ $S_2:\{a^nb^n|n\geq 1\} \cup \{a^nb^m|n \geq1,m \geq 1\} $ Which of the following is regular? $S_1$ only $S_2$ only Both Neither of the above
asked
May 26, 2019
in
Theory of Computation
Hirak
772
views
made-easy-test-series
theory-of-computation
regular-languages
0
votes
1
answer
16
self doubt: TOC
is union of regular language and context free language always regular?
is union of regular language and context free language always regular?
asked
May 22, 2019
in
Theory of Computation
Hirak
125
views
theory-of-computation
regular-languages
context-free-languages
3
votes
1
answer
17
Self Doubt : Ambiguity
Why is ambiguity in regular language is decidable and not decidable in CFL ? Can you give Example?
Why is ambiguity in regular language is decidable and not decidable in CFL ? Can you give Example?
asked
May 10, 2019
in
Theory of Computation
logan1x
344
views
theory-of-computation
finite-automata
ambiguous
regular-languages
context-free-languages
context
0
votes
0
answers
18
Michael Sipser Edition 3 Exercise 2 Question 20 (Page No. 156)
Let $A/B = \{w\mid wx\in A$ $\text{for some}$ $x \in B\}.$ Show that if $A$ is context free and $B$ is regular$,$ then $A/B$ is context free$.$
Let $A/B = \{w\mid wx\in A$ $\text{for some}$ $x \in B\}.$ Show that if $A$ is context free and $B$ is regular$,$ then $A/B$ is context free$.$
asked
May 4, 2019
in
Theory of Computation
Lakshman Patel RJIT
59
views
michael-sipser
theory-of-computation
context-free-languages
regular-languages
0
votes
1
answer
19
Michael Sipser Edition 3 Exercise 2 Question 18 (Page No. 156)
Let $C$ be a context-free language and $R$ be a regular language$.$ Prove that the language $C\cap R$ is context-free. Let $A = \{w\mid w\in \{a, b, c\}^{*}$ $\text{and}$ $w$ $\text{contains equal numbers of}$ $a’s, b’s,$ $\text{and}$ $c’s\}.$ Use $\text{part (a)}$ to show that $A$ is not a CFL$.$
Let $C$ be a context-free language and $R$ be a regular language$.$ Prove that the language $C\cap R$ is context-free. Let $A = \{w\mid w\in \{a, b, c\}^{*}$ $\text{and}$ $w$ $\text{contains equal numbers of}$ $a’s, b’s,$ $\text{and}$ $c’s\}.$ Use $\text{part (a)}$ to show that $A$ is not a CFL$.$
asked
May 4, 2019
in
Theory of Computation
Lakshman Patel RJIT
64
views
michael-sipser
theory-of-computation
context-free-languages
regular-languages
0
votes
0
answers
20
Michael Sipser Edition 3 Exercise 2 Question 17 (Page No. 156)
Use the results of $\text{Question 16}$ to give another proof that every regular language is context free$,$ by showing how to convert a regular expression directly to an equivalent context-free grammar$.$
Use the results of $\text{Question 16}$ to give another proof that every regular language is context free$,$ by showing how to convert a regular expression directly to an equivalent context-free grammar$.$
asked
May 4, 2019
in
Theory of Computation
Lakshman Patel RJIT
44
views
michael-sipser
theory-of-computation
regular-languages
context-free-languages
0
votes
1
answer
21
Michael Sipser Edition 3 Exercise 2 Question 13 (Page No. 156)
Let $G = (V, \Sigma, R, S)$ be the following grammar. $V = \{S, T, U\}; \Sigma = \{0, \#\};$ and $R$ is the set of rules$:$ $S\rightarrow TT\mid U$ $T\rightarrow 0T\mid T0\mid \#$ $U\rightarrow 0U00\mid\#$ Describe $L(G)$ in English. Prove that $L(G)$ is not regular$.$
Let $G = (V, \Sigma, R, S)$ be the following grammar. $V = \{S, T, U\}; \Sigma = \{0, \#\};$ and $R$ is the set of rules$:$ $S\rightarrow TT\mid U$ $T\rightarrow 0T\mid T0\mid \#$ $U\rightarrow 0U00\mid\#$ Describe $L(G)$ in English. Prove that $L(G)$ is not regular$.$
asked
May 4, 2019
in
Theory of Computation
Lakshman Patel RJIT
103
views
michael-sipser
theory-of-computation
context-free-grammars
regular-languages
0
votes
0
answers
22
Michael Sipser Edition 3 Exercise 1 Question 72 (Page No. 93)
Let $M_{1}$ and $M_{2}$ be $\text{DFA's}$ that have $k_{1}$ and $k_{2}$ states, respectively, and then let $U = L(M_{1})\cup L(M_{2}).$ Show that if $U\neq\phi$ then $U$ contains some string $s,$ where $|s| < max(k1, k2).$ Show that if $U\neq\sum^{*},$ then $U$ excludes some string $s,$ where $|s| < k1k2.$
Let $M_{1}$ and $M_{2}$ be $\text{DFA's}$ that have $k_{1}$ and $k_{2}$ states, respectively, and then let $U = L(M_{1})\cup L(M_{2}).$ Show that if $U\neq\phi$ then $U$ contains some string $s,$ where $|s| < max(k1, k2).$ Show that if $U\neq\sum^{*},$ then $U$ excludes some string $s,$ where $|s| < k1k2.$
asked
Apr 30, 2019
in
Theory of Computation
Lakshman Patel RJIT
120
views
michael-sipser
theory-of-computation
finite-automata
regular-languages
proof
descriptive
2
votes
1
answer
23
Michael Sipser Edition 3 Exercise 1 Question 71 (Page No. 93)
Let $\sum = \{0,1\}$ Let $A=\{0^{k}u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$ Show that $A$ is regular. Let $B=\{0^{k}1u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$Show that $B$ is not regular.
Let $\sum = \{0,1\}$ Let $A=\{0^{k}u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$ Show that $A$ is regular. Let $B=\{0^{k}1u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$Show that $B$ is not regular.
asked
Apr 30, 2019
in
Theory of Computation
Lakshman Patel RJIT
131
views
michael-sipser
theory-of-computation
finite-automata
regular-languages
proof
descriptive
0
votes
1
answer
24
Michael Sipser Edition 3 Exercise 1 Question 70 (Page No. 93)
We define the $\text{avoids}$ operation for languages $A$ and $B$ to be $\text{A avoids B = {w| w ∈ A and w doesn’t contain any string in B as a substring}.}$ Prove that the class of regular languages is closed under the ${avoids}$ operation.
We define the $\text{avoids}$ operation for languages $A$ and $B$ to be $\text{A avoids B = {w| w ∈ A and w doesn’t contain any string in B as a substring}.}$ Prove that the class of regular languages is closed under the ${avoids}$ operation.
asked
Apr 30, 2019
in
Theory of Computation
Lakshman Patel RJIT
166
views
michael-sipser
theory-of-computation
finite-automata
regular-languages
proof
descriptive
0
votes
0
answers
25
Michael Sipser Edition 3 Exercise 1 Question 68 (Page No. 93)
In the traditional method for cutting a deck of playing cards, the deck is arbitrarily split two parts, which are exchanged beforereassembling the deck. In a more complex cut, called $\text{Scarne's cut,}$ the deck is broken into three parts ... $ CUT(CUT(B)).}$ Show that the class of regular languages is closed under $\text{CUT}.$
In the traditional method for cutting a deck of playing cards, the deck is arbitrarily split two parts, which are exchanged beforereassembling the deck. In a more complex cut, called $\text{Scarne's cut,}$ the deck is broken into three parts and the middle part in placed first in the ... which $\text{CUT(B)$\neq$ CUT(CUT(B)).}$ Show that the class of regular languages is closed under $\text{CUT}.$
asked
Apr 30, 2019
in
Theory of Computation
Lakshman Patel RJIT
134
views
michael-sipser
theory-of-computation
regular-languages
scarnes-cut
proof
descriptive
0
votes
0
answers
26
Michael Sipser Edition 3 Exercise 1 Question 67 (Page No. 93)
Let the rotational closure of language $A$ be $RC(A) = \{yx| xy ∈ A\}.$ Show that for any language $A,$ we have $RC(A) = RC(RC(A)).$ Show that the class of regular languages is closed under rotational closure.
Let the rotational closure of language $A$ be $RC(A) = \{yx| xy ∈ A\}.$ Show that for any language $A,$ we have $RC(A) = RC(RC(A)).$ Show that the class of regular languages is closed under rotational closure.
asked
Apr 30, 2019
in
Theory of Computation
Lakshman Patel RJIT
111
views
michael-sipser
theory-of-computation
regular-languages
rotational-closure-of-language
descriptive
0
votes
0
answers
27
Michael Sipser Edition 3 Exercise 1 Question 63 (Page No. 92)
Let $A$ be an infinite regular language. Prove that $A$ can be split into two infinite disjoint regular subsets. Let $B$ and $D$ be two languages. Write $B\subseteqq D$ if $B\subseteq D$ and $D$ contains infinitely many ... regular languages where $B\subseteqq D,$ then we can find a regular language $C$ where $B\subseteqq C\subseteqq D.$
Let $A$ be an infinite regular language. Prove that $A$ can be split into two infinite disjoint regular subsets. Let $B$ and $D$ be two languages. Write $B\subseteqq D$ if $B\subseteq D$ and $D$ contains infinitely many strings that are not in $B.$ Show that if $B$ and $D$ are two regular languages where $B\subseteqq D,$ then we can find a regular language $C$ where $B\subseteqq C\subseteqq D.$
asked
Apr 30, 2019
in
Theory of Computation
Lakshman Patel RJIT
83
views
michael-sipser
theory-of-computation
finite-automata
regular-languages
descriptive
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