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Recent questions tagged closure-property
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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.
GO Classes
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in
Theory of Computation
Feb 5
by
GO Classes
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goclasses2024-mockgate-14
theory-of-computation
closure-property
multiple-selects
1-mark
3
votes
2
answers
2
TOC - Self Doubt
Can anyone explain $\overline{ww}$ is $CFL$ or $CSL$ And if $CFL$ can you write the equivalent $CFG$ for this ?
Jiten008
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in
Theory of Computation
Oct 24, 2023
by
Jiten008
360
views
pushdown-automata
theory-of-computation
self-doubt
regular-language
context-free-language
context-sensitive
turing-machine
closure-property
context-free-grammar
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?
Sunnidhya Roy
asked
in
Theory of Computation
Dec 11, 2022
by
Sunnidhya Roy
373
views
theory-of-computation
closure-property
regular-language
0
votes
0
answers
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 ?
Shreya2002
asked
in
Theory of Computation
Dec 1, 2022
by
Shreya2002
308
views
theory-of-computation
regular-language
closure-property
made-easy-test-series
0
votes
2
answers
5
ACE 2023 Test series: TOC: Basic properties
abhinowKatore
asked
in
Theory of Computation
Oct 18, 2022
by
abhinowKatore
690
views
theory-of-computation
regular-expression
closure-property
ace-test-series
1
vote
1
answer
6
Igate Test Series
please explain all options with example
SKMAKM
asked
in
Theory of Computation
Jul 20, 2022
by
SKMAKM
588
views
decidability
closure-property
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
admin
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in
Theory of Computation
Oct 12, 2019
by
admin
317
views
michael-sipser
theory-of-computation
context-free-language
closure-property
descriptive
0
votes
0
answers
8
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 $CUT$.
admin
asked
in
Theory of Computation
Oct 12, 2019
by
admin
210
views
michael-sipser
theory-of-computation
context-free-language
closure-property
descriptive
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.
admin
asked
in
Theory of Computation
Oct 12, 2019
by
admin
1.3k
views
michael-sipser
theory-of-computation
context-free-language
closure-property
descriptive
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
gatecse
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in
Theory of Computation
Sep 13, 2019
by
gatecse
867
views
cmi2019
regular-language
context-free-language
closure-property
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?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 12, 2019
by
Naveen Kumar 3
389
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 12, 2019
by
Naveen Kumar 3
389
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 12, 2019
by
Naveen Kumar 3
190
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 12, 2019
by
Naveen Kumar 3
219
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
1
vote
1
answer
15
Peter Linz Edition 4 Exercise 4.3 Question 16 (Page No. 123)
Is the following language regular? $L=$ {$w_1cw_2:w_1,w_2∈$ {$a,b$}$^*,w_1\neq w_2$}.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 12, 2019
by
Naveen Kumar 3
304
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
1
vote
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) $L=$ {$a^nb^l:|n-l|=2$}
Naveen Kumar 3
asked
in
Theory of Computation
Apr 12, 2019
by
Naveen Kumar 3
301
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
pumping-lemma
closure-property
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. $L=$ {$a^nb^k:n>k$} $\cup$ {$a^nb^k:n\neq k-1$}.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
281
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
243
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
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) $L (G_1)^*$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
260
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
182
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
214
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
240
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
301
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
1
vote
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.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
362
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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