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Recent questions tagged closure-property
2
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0
answers
1
#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
91
views
theory-of-computation
closure-property
regular-language
0
votes
0
answers
2
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 2, 2022
by
Shreya2002
114
views
theory-of-computation
regular-language
closure-property
made-easy-test-series
0
votes
2
answers
3
ACE 2023 Test series: TOC: Basic properties
abhinowKatore
asked
in
Theory of Computation
Oct 18, 2022
by
abhinowKatore
237
views
theory-of-computation
regular-expression
closure-property
ace-test-series
1
vote
1
answer
4
Igate Test Series
please explain all options with example
Amit Mehta
asked
in
Theory of Computation
Jul 20, 2022
by
Amit Mehta
255
views
decidability
closure-property
0
votes
1
answer
5
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
Lakshman Patel RJIT
asked
in
Theory of Computation
Oct 13, 2019
by
Lakshman Patel RJIT
226
views
michael-sipser
theory-of-computation
context-free-language
closure-property
descriptive
0
votes
0
answers
6
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 $CUT$.
Lakshman Patel RJIT
asked
in
Theory of Computation
Oct 13, 2019
by
Lakshman Patel RJIT
145
views
michael-sipser
theory-of-computation
context-free-language
closure-property
descriptive
0
votes
1
answer
7
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.
Lakshman Patel RJIT
asked
in
Theory of Computation
Oct 13, 2019
by
Lakshman Patel RJIT
728
views
michael-sipser
theory-of-computation
context-free-language
closure-property
descriptive
2
votes
3
answers
8
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
asked
in
Theory of Computation
Sep 13, 2019
by
gatecse
618
views
cmi2019
regular-language
context-free-language
closure-property
0
votes
2
answers
9
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
260
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
2
answers
10
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
221
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
11
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
131
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
12
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
135
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
1
vote
1
answer
13
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
204
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
0
votes
0
answers
14
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
223
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
pumping-lemma
closure-property
0
votes
1
answer
15
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
227
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
2
votes
0
answers
16
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
188
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
0
votes
0
answers
17
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
125
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
18
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
118
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
19
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
143
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 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
187
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 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
170
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
1
vote
0
answers
22
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
239
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 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
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
158
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
24
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
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
135
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
25
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
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
142
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
26
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
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
101
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
27
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
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
99
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
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