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Recent questions tagged closure-property
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31
Peter Linz Edition 4 Exercise 4.1 Question 20 (Page No. 110)
For a string $a_1a_2…a_n$ define the operation $shift$ as $shift(a_1a_2...a_n)=a_2a_3...a_na_1$ From this, we can define the operation on a language as $shift(L)=$ {$v:v=shift(w$ for some $w∈L$} Show that regularity is preserved under the shift operation.
Naveen Kumar 3
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Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
294
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
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0
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32
Peter Linz Edition 4 Exercise 4.1 Question 19 (Page No. 110)
Define an operation $third$ on strings and languages as $third(a_1a_2a_3a_4a_5a_6...)=a_3a_6...$ with the appropriate extension of this definition to languages. Prove the closure of the family of regular languages under this operation.
Naveen Kumar 3
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Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
282
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
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0
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33
Peter Linz Edition 4 Exercise 4.1 Question 18 (Page No. 110)
The $head$ of a language is the set of all prefixes of its strings, that is, $head(L)=$ {$x:xy∈L$ for some $y ∈Σ^*$} Show that the family of regular languages is closed under this operation.
Naveen Kumar 3
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in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
224
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
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0
answers
34
Peter Linz Edition 4 Exercise 4.1 Question 17 (Page No. 110)
The $tail$ of a language is defined as the set of all suffixes of its strings, that is, $tail(L)=$ {$y:xy∈L$ for some $x∈Σ^*$} Show that if L is regular, so is $tail(L)$.
Naveen Kumar 3
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in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
155
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
35
Peter Linz Edition 4 Exercise 4.1 Question 16 (Page No. 110)
Show that if the statement “If $L_1$ is regular and $L_1 ∪ L_2$ is also regular, then $L_2$ must be regular“ were true for all $L_1$ and $L_2$, then all languages would be regular.
Naveen Kumar 3
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in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
149
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
36
Peter Linz Edition 4 Exercise 4.1 Question 15 (Page No. 110)
The left quotient of a language $L_1$ with respect to $L_2$ is defined as $L_2/L_1=$ {$y:x∈L_2,xy∈L_1$} Show that the family of regular languages is closed under the left quotient with a regular language.
Naveen Kumar 3
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in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
202
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
1
answer
37
Peter Linz Edition 4 Exercise 4.1 Question 14 (Page No. 109)
If $L$ is a regular language, prove that the language {$uv : u ∈ L,υ ∈ L^R$} is also regular.
Naveen Kumar 3
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in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
218
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
1
answer
38
Peter Linz Edition 4 Exercise 4.1 Question 13 (Page No. 109)
If $L$ is a regular language, prove that $L_1 =$ {$uv : u ∈ L, |υ| = 2$} is also regular.
Naveen Kumar 3
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in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
189
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
39
Peter Linz Edition 4 Exercise 4.1 Question 12 (Page No. 109)
Suppose we know that $L_1 ∪ L_2$ is regular and that $L_1$ is finite. Can we conclude from this that $L_2$ is regular?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
180
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
40
Peter Linz Edition 4 Exercise 4.1 Question 11 (Page No. 109)
Show that $L_1 = L_1L_2/L_2$ is not true for all languages $L_1$ and $L_2$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
208
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
41
Peter Linz Edition 4 Exercise 4.1 Question 10 (Page No. 109)
Let $L_1 = L (a^*baa^*)$ and $L_2 = L (aba^*)$. Find $L_1/L_2$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
171
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
42
Peter Linz Edition 4 Exercise 4.1 Question 9 (Page No. 109)
Which of the following are true for all regular languages and all homomorphisms? (a) $h (L_1 ∪ L_2)= h (L_1) ∩ h (L_2)$. (b) $h (L_1 ∩ L_2)= h (L_1) ∩ h (L_2)$. (c) $h (L_1L_2) = h (L_1) h (L_2)$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
204
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
43
Peter Linz Edition 4 Exercise 4.1 Question 8 (Page No. 109)
Define the $complementary$ or $(cor)$ of two languages by $cor(L_1,L_2)=$ {$w:w∈\overline{L_1}$ or $w∈\overline{L_2}$} Show that the family of regular languages is closed under the $cor$ operation.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
190
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
44
Peter Linz Edition 4 Exercise 4.1 Question 7 (Page No. 109)
The $nor$ of two languages is $nor(L_1,L_2)=$ {$w:w∉L_1$ and $w∉L_2$} Show that the family of regular languages is closed under the $nor$ operation.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
119
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
45
Peter Linz Edition 4 Exercise 4.1 Question 6 (Page No. 109)
The symmetric difference of two sets $S_1$ and $S_2$ is defined as $S_1 θ S_2 =$ {$x: x ∈ S_1$ or $x ∈ S_2,$ but $x$ is not in both $S_1$ and $S_2$}. Show that the family of regular languages is closed under symmetric difference.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
146
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
46
Peter Linz Edition 4 Exercise 4.1 Question 5 (Page No. 109)
Show that the family of regular languages is closed under finite union and intersection, that is, if $L_1,L_2,…, L_n$ are regular, then $L_U=\bigcup_{i=1,2,..,n}$L_i$ and $L_I=\bigcap_{i=1,2,3,...,n}L_i$ are also regular.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
155
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
47
Peter Linz Edition 4 Exercise 4.1 Question 3 (Page No. 108)
“The family of regular languages is closed under difference.” Provide constructive proof for this argument.
Naveen Kumar 3
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Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
147
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
1
answer
48
Peter Linz Edition 4 Exercise 4.1 Question 2 (Page No. 108)
Find nfa's that accept (a) $L ((a + b) a^*) ∩ L (baa^*)$. (b) $L (ab^*a^*) ∩ L (a^*b^*a)$.
Naveen Kumar 3
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in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
445
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
1
vote
1
answer
49
MadeEasy Subject Test 2019: Theory of Computation - Closure Property
Consider the following Statements : There Exist a non-deterministic CFL whose reversal is DCFL. There exist a non regular CSL whose Kleene Closure is regular. Which of following are True ? Explain with reasons.
Na462
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in
Theory of Computation
Jan 13, 2019
by
Na462
1.1k
views
theory-of-computation
closure-property
made-easy-test-series
0
votes
0
answers
50
MadeEasy Test Series: Theory Of Computation - Closure Property
L1 is regular, L2 and L3 are CFL L1 is regular, L2 is CFL and L3 is CSL L1 is CFL but not regular,L2 is CSL but not CFL,L3 is CFL L1, L2 and L3 are CFL
Sambhrant Maurya
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in
Theory of Computation
Jan 9, 2019
by
Sambhrant Maurya
525
views
made-easy-test-series
regular-language
context-free-language
closure-property
4
votes
1
answer
51
GATE Overflow | Mock GATE | Test 1 | Question: 56
Consider the following language $L$: $L=\{<M,x,k> \mid M \text{ is a Turing Machine and M does not halt on x within k steps} \}$ The language family to which $L$ belongs is not closed under? Intersection Homomorphism Set Difference Complementation
Ruturaj Mohanty
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in
Theory of Computation
Dec 27, 2018
by
Ruturaj Mohanty
1.6k
views
go-mockgate-1
recursive-and-recursively-enumerable-languages
theory-of-computation
turing-machine
closure-property
4
votes
1
answer
52
Closure Properties
What is difference between Σ* and L* ? Which is true ? S1 : Σ* – {ϵ} = Σ+ S2 : L* – {ϵ} = L+ .
anurag sharma
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in
Theory of Computation
Dec 24, 2018
by
anurag sharma
1.9k
views
theory-of-computation
closure-property
regular-language
0
votes
0
answers
53
proving a language is regular based on two regular language over same $\Sigma$ (complicated)
Hello, I've encountered with a difficult question i don't know how to solve. the question is about proving that a language is regular based on two language over the same $\Sigma$. the questions goes ... know it's complicated and would appreciate help with it. thank you very much your much appreciated help!
csenoob
asked
in
Theory of Computation
Dec 8, 2018
by
csenoob
212
views
regular-language
theory-of-computation
finite-automata
closure-property
1
vote
0
answers
54
Closure Property
If L1 is CSL and L2 is CFL, then which of the following is correct ? A.L1' - L2 is CSL always B. L1 - L2' is CSL always C. L1 intersection Regular is Regular always D. L1.L2 is CSL but not CFL
Na462
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Theory of Computation
Sep 9, 2018
by
Na462
1.9k
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theory-of-computation
context-free-language
closure-property
0
votes
0
answers
55
Relationship b/w closure and decidability?
Is there any relationship b/w closure and decidability? Thanks
surbhijain93
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in
Theory of Computation
Sep 9, 2018
by
surbhijain93
311
views
theory-of-computation
decidability
closure-property
0
votes
0
answers
56
self doubt
CAN SOMEONE EXPLAIN ME WITH AN EXAMPLE THAT WHY DCFL CLOSED UNDER COMPLEMENATION AND CFL NOT CLOSED UNDER COMPLEMENATION?
sushmita
asked
in
Theory of Computation
Sep 9, 2018
by
sushmita
181
views
theory-of-computation
closure-property
decidability
0
votes
2
answers
57
Theory of computation - Closure Property
Cfl is closed under intersection with regular language. Then resultant languages will be regular or cfl ? Let X is cfl Y is regular language L=X intersection Y Then L is what?
Dhoomketu
asked
in
Theory of Computation
May 10, 2018
by
Dhoomketu
607
views
theory-of-computation
closure-property
4
votes
2
answers
58
ISRO2018-25
$CFG$ (Context Free Grammar) is not closed under: Union Complementation Kleene star Product
Arjun
asked
in
Theory of Computation
Apr 22, 2018
by
Arjun
1.6k
views
isro2018
closure-property
context-free-language
theory-of-computation
27
votes
6
answers
59
GATE CSE 2018 | Question: 7
The set of all recursively enumerable languages is: closed under complementation closed under intersection a subset of the set of all recursive languages an uncountable set
gatecse
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in
Theory of Computation
Feb 14, 2018
by
gatecse
11.4k
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gatecse-2018
theory-of-computation
closure-property
easy
1-mark
0
votes
0
answers
60
Kenneth Rosen Edition 6th Exercise 7.4 (Page No. 488)
Let R be a relation on a set A. R may or may not have some property P, such as reflexivity, symmetry, or transitivity. If there is a relation S with property P containing R such that S is a subset of every relation with ... R, then S is called the closure Relations of R with respect to P. can someone explain this definition in simple words?
Mk Utkarsh
asked
in
Set Theory & Algebra
Feb 14, 2018
by
Mk Utkarsh
412
views
discrete-mathematics
kenneth-rosen
set-theory&algebra
closure-property
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