Recent questions tagged closure-property / GATE Overflow for GATE CSE

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GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 31
DeMorgan's Laws ensure that Closure under intersection and complementation imply closure under union. Closure under intersection and union imply closure under complementation. Closure under union and complementation imply closure ... Closure under any two of union, intersection, and complementation implies closure under all three.

DeMorgan’s Laws ensure thatClosure under intersection and complementation imply closure under union.Closure under intersection and union imply closure under complementa...

GO Classes

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GO Classes asked Feb 5

3 votes

2 answers

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TOC - Self Doubt
Can anyone explain $\overline{ww}$ is $CFL$ or $CSL$ And if $CFL$ can you write the equivalent $CFG$ for this ?

Can anyone explain $\overline{ww}$ is $CFL$ or $CSL$ And if $CFL$ can you write the equivalent $CFG$ for this ?

Jiten008

367 views

Jiten008 asked Oct 24, 2023

2 votes

0 answers

3

#Self Doubt
Suppose L1 = CFL and L2 = Regular, We are to find out whether L1 - L2 = CFL or non CFL. I have 2 approaches to this question and I am confused which is wrong: L1 - L2 = L1 intersection L2' L2 being Regular L2' is also Regular so CFL ... being Regular L2' is also Regular and every Regular Language is also CFL so CFL intersection CFL = non CFL. Can somebody please clarify my doubt?

Suppose L1 = CFL and L2 = Regular, We are to find out whether L1 – L2 = CFL or non CFL.I have 2 approaches to this question and I am confused which is wrong:L1 – L2 =...

Sunnidhya Roy

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Sunnidhya Roy asked Dec 11, 2022

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4

Made easy Theory of Computation
Which of them are not regular- (a) L={a^m b^n | n>=2023, m<=2023} (b) L={a^n b^m c^l | n=2023, m>2023, l>m} according made easy (b) is the answer but can we do like this- Let L1= {a^n |n=2023} ... ) and so L2 is regular L=L1.L2 (regular lang are closed under concatenation) therefore L is regular.this makes option (b) regular is it right approach ?

Which of them are not regular-(a) L={a^m b^n | n>=2023, m<=2023}(b) L={a^n b^m c^l | n=2023, m>2023, l>m}according made easy (b) is the answer but can we do like this-Let...

Shreya2002

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Shreya2002 asked Dec 1, 2022

0 votes

2 answers

5

ACE 2023 Test series: TOC: Basic properties

abhinowKatore

690 views

abhinowKatore asked Oct 18, 2022

1 votes

1 answer

6

Igate Test Series
please explain all options with example

please explain all options with example

SKMAKM

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SKMAKM asked Jul 20, 2022

0 votes

1 answer

7

Michael Sipser Edition 3 Exercise 2 Question 53 (Page No. 159)
Show that the class of DCFLs is not closed under the following operations: Union Intersection Concatenation Star Reversal

Show that the class of DCFLs is not closed under the following operations:UnionIntersectionConcatenationStarReversal

admin

321 views

admin asked Oct 12, 2019

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Michael Sipser Edition 3 Exercise 2 Question 50 (Page No. 159)
We defined the $CUT$ of language $A$ to be $CUT(A) = \{yxz| xyz \in A\}$. Show that the class of $CFLs$ is not closed under $CUT$.

We defined the $CUT$ of language $A$ to be $CUT(A) = \{yxz| xyz \in A\}$. Show that the class of $CFLs$ is not closed under $CUT$.

admin

230 views

admin asked Oct 12, 2019

0 votes

1 answer

9

Michael Sipser Edition 3 Exercise 2 Question 49 (Page No. 159)
We defined the rotational closure of language $A$ to be $RC(A) = \{yx \mid xy \in A\}$.Show that the class of CFLs is closed under rotational closure.

We defined the rotational closure of language $A$ to be $RC(A) = \{yx \mid xy \in A\}$.Show that the class of CFLs is closed under rotational closure.

admin

1.4k views

admin asked Oct 12, 2019

2 votes

3 answers

10

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...

gatecse

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gatecse asked Sep 13, 2019

0 votes

2 answers

11

Peter Linz Edition 4 Exercise 4.3 Question 24 (Page No. 124)
Suppose that we know that $L_1 ∪ L_2$ and $L_1$ are regular. Can we conclude from this that $L_2$ is regular?

Suppose that we know that $L_1 ∪ L_2$ and $L_1$ are regular. Can we conclude from this that $L_2$ is regular?

Naveen Kumar 3

397 views

Naveen Kumar 3 asked Apr 12, 2019

0 votes

2 answers

12

Peter Linz Edition 4 Exercise 4.3 Question 23 (Page No. 124)
Is the family of regular languages closed under infinite intersection?

Is the family of regular languages closed under infinite intersection?

Naveen Kumar 3

409 views

Naveen Kumar 3 asked Apr 12, 2019

0 votes

0 answers

13

Peter Linz Edition 4 Exercise 4.3 Question 22 (Page No. 124)
Consider the argument that the language associated with any generalized transition graph is regular. The language associated with such a graph is $L=\bigcup_{p∈P} L(r_p)$, where $P$ ... is regular. Show that in this case, because of the special nature of $P$, the infinite union is regular.

Consider the argument that the language associated with any generalized transition graph is regular. The language associated with such a graph is $L=\bigcu...

Naveen Kumar 3

201 views

Naveen Kumar 3 asked Apr 12, 2019

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0 answers

14

Peter Linz Edition 4 Exercise 4.3 Question 21 (Page No. 124)
Let $P$ be an infinite but countable set, and associate with each $p ∈ P$ a language $L_p$. The smallest set containing every $L_p$ is the union over the infinite set $P$; it will be denoted by $U_{p∈p}L_p$. Show by example that the family of regular languages is not closed under infinite union.

Let $P$ be an infinite but countable set, and associate with each $p ∈ P$ a language $L_p$. The smallest set containing every $L_p$ is the union over the infinite set $...

Naveen Kumar 3

218 views

Naveen Kumar 3 asked Apr 12, 2019

1 votes

1 answer

15

Peter Linz Edition 4 Exercise 4.3 Question 16 (Page No. 123)
Is the following language regular? $L=$ {$w_1cw_2:w_1,w_2∈$ {$a,b$}$^*,w_1\neq w_2$}.

Is the following language regular? $L=$ {$w_1cw_2:w_1,w_2∈$ {$a,b$}$^*,w_1\neq w_2$}.

Naveen Kumar 3

326 views

Naveen Kumar 3 asked Apr 12, 2019

1 votes

0 answers

16

Peter Linz Edition 4 Exercise 4.3 Question 15 (Page No. 123)
Consider the languages below. For each, make a conjecture whether or not it is regular. Then prove your conjecture. (a) $L=$ {$a^nb^la^k:n+k+l \gt 5$} (b) $L=$ {$a^nb^la^k:n \gt 5,l> 3,k\leq l$} (c) $L=$ {$a^nb^l:n/l$ is an integer} (d) $L=$ ... $L=$ {$a^nb^l:n\geq 100,l\leq 100$} (g) $L=$ {$a^nb^l:|n-l|=2$}

Consider the languages below. For each, make a conjecture whether or not it is regular. Thenprove your conjecture.(a) $L=$ {$a^nb^la^k:n+k+l \gt 5$}(b) $L=$ {$a^nb^la^k:n...

Naveen Kumar 3

312 views

Naveen Kumar 3 asked Apr 12, 2019

0 votes

1 answer

17

Peter Linz Edition 4 Exercise 4.3 Question 13 (Page No. 123)
Show that the following language is not regular. $L=$ {$a^nb^k:n>k$} $\cup$ {$a^nb^k:n\neq k-1$}.

Show that the following language is not regular.$L=$ {$a^nb^k:n>k$} $\cup$ {$a^nb^k:n\neq k-1$}.

Naveen Kumar 3

285 views

Naveen Kumar 3 asked Apr 11, 2019

2 votes

0 answers

18

Peter Linz Edition 4 Exercise 4.3 Question 10 (Page No. 123)
Consider the language $L=$ {$a^n:n$ is not a perfect square}. (a) Show that this language is not regular by applying the pumping lemma directly. (b) Then show the same thing by using the closure properties of regular languages.

Consider the language $L=$ {$a^n:n$ is not a perfect square}.(a) Show that this language is not regular by applying the pumping lemma directly.(b) Then show the same thin...

Naveen Kumar 3

246 views

Naveen Kumar 3 asked Apr 11, 2019

0 votes

0 answers

19

Peter Linz Edition 4 Exercise 4.1 Question 26 (Page No. 110)
Let $G_1$ and $G_2$ be two regular grammars. Show how one can derive regular grammars for the languages (a) $L (G_1) ∪ L (G_2)$. (b) $L (G_1) L (G_2)$. (b) $L (G_1)^*$.

Let $G_1$ and $G_2$ be two regular grammars. Show how one can derive regular grammars for the languages(a) $L (G_1) ∪ L (G_2)$.(b) $L (G_1) L (G_2)$.(b) $L (G_1)^*$.

Naveen Kumar 3

270 views

Naveen Kumar 3 asked Apr 5, 2019

0 votes

0 answers

20

Peter Linz Edition 4 Exercise 4.1 Question 25 (Page No. 111)
The $min$ of a language $L$ is defined as $min(L)=$ {$w∈L:$ there is no $u∈L,v∈Σ^+,$ such that $w=uv$} Show that the family of regular languages is closed under the $ min$ operation.

The $min$ of a language $L$ is defined as $min(L)=$ {$w∈L:$ there is no $u∈L,v∈Σ^+,$ such that $w=uv$}Show that the family of regular languages is closed ...

Naveen Kumar 3

182 views

Naveen Kumar 3 asked Apr 5, 2019

0 votes

0 answers

21

Peter Linz Edition 4 Exercise 4.1 Question 24 (Page No. 111)
Define the operation $leftside$ on $L$ by $leftside(L)=$ {$w:ww^R∈L$} Is the family of regular languages closed under this operation?

Define the operation $leftside$ on $L$ by $leftside(L)=$ {$w:ww^R∈L$}Is the family of regular languages closed under this operation?

Naveen Kumar 3

219 views

Naveen Kumar 3 asked Apr 5, 2019

0 votes

0 answers

22

Peter Linz Edition 4 Exercise 4.1 Question 23 (Page No. 111)
Define an operation $minus5$ on a language $L$ as the set of all strings of $L$ with the fifth symbol from the left removed (strings of length less than five are left unchanged). Show that the family of regular languages is closed under the $minus5$ operation.

Define an operation $minus5$ on a language $L$ as the set of all strings of $L$ with the fifth symbol from the left removed (strings of length less than five are left unc...

Naveen Kumar 3

243 views

Naveen Kumar 3 asked Apr 5, 2019

0 votes

0 answers

23

Peter Linz Edition 4 Exercise 4.1 Question 22 (Page No. 110)
The $\textit{shuffle}$ of two languages $L_1$ and $L_2$ is defined as $\textit{shuffle}(L_1,L_2)= \{w_1v_1w_2v_2w_3v_3...w_mv_m:w_1w_2w_3….w_m∈L_1, v_1v_2...v_m∈L_2,\text{ for all }w_i,v_i∈Σ^*\}.$ Show that the family of regular languages is closed under the $shuffle$ operation.

The $\textit{shuffle}$ of two languages $L_1$ and $L_2$ is defined as $\textit{shuffle}(L_1,L_2)= \{w_1v_1w_2v_2w_3v_3...w_mv_m:w_1w_2w_3….w_m∈L_1, v_1v_2...v_m∈L_2...

Naveen Kumar 3

314 views

Naveen Kumar 3 asked Apr 5, 2019

1 votes

0 answers

24

Peter Linz Edition 4 Exercise 4.1 Question 21 (Page No. 110)
Define $exchange(a_1a_2a_3...a_{n-1}a_n)=a_na_2a_3...a_{n-1}a_1$, and $exchange(L)=$ {$v:v=exchange(w)$ for some $w∈L$} Show that the family of regular languages is closed under exchange.

Define$exchange(a_1a_2a_3...a_{n-1}a_n)=a_na_2a_3...a_{n-1}a_1$,and$exchange(L)=$ {$v:v=exchange(w)$ for some $w∈L$}Show that the family of regular languages is closed ...

Naveen Kumar 3

373 views

Naveen Kumar 3 asked Apr 5, 2019

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