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Recent questions tagged pumping-lemma
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Pumping Lemma
Use the Pumping Lemma to show that the following languages over Σ={�,�}Σ={a,b} are not regular. In each case, carefully describe the string that will be pumped and explain why pumping it leads to a contradiction. {aaabnan∣n≥0} {ww∣w∈Σ∗}
jg662
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in
Theory of Computation
Feb 22
by
jg662
66
views
theory-of-computation
pumping-lemma
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0
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2
Pumping Lemma
If there is a w’ such that w’ ∉ L in the final step of pumping lemma, then L is not regular (Lemma fails) Can we conversely say for certain if L is not regular, then definitely there is a w’ ∉ L. Simply : Can there be a case where we have all w’ ∈ L and still language is not regular?
Mrityudoot
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in
Theory of Computation
Nov 8, 2023
by
Mrityudoot
132
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theory-of-computation
pumping-lemma
regular-language
0
votes
0
answers
3
Theory Of Computation | Minimum Pumping Length | MPL
MSQ Consider the following languages and their MPL (Minimum Pumping Length) Which among these are TRUE: L1 = aa(b)* :: MPL(L1) = 3 L2 = aa(aa)* :: MPL(L2) = 2 L2 = aa(aa)* :: MPL(L2) = 3 L2 = aa(aa)* :: MPL(L2) = 4 L3 = aa(ab)* :: MPL(L3) = 4 L4 = aa(b)* + aad(c)* :: MPL(L4) = 4
Souvik33
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in
Theory of Computation
Jan 7, 2023
by
Souvik33
659
views
theory-of-computation
pumping-lemma
0
votes
1
answer
4
#Self Doubt
L = {0^n 1^2n 0^n+m , n,m>=0} Is this Language CFL or non CFL? According to me we can write this as 0^n 1^n 1^n 0^n 0^m Then we will keep on pushing 0's and as and when we get 1 we keep on popping 0's, now once the stack is ... then on seeing any number of 0's we don't push anything and when we reach the end of the string we simply move to the final state. Is this logic correct?
Sunnidhya Roy
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in
Theory of Computation
Dec 12, 2022
by
Sunnidhya Roy
581
views
theory-of-computation
dcfl
pumping-lemma
context-free-language
0
votes
1
answer
5
Pumping Lemma
If L = { x == y | where x and y are equal binary numbers} and Σ = {0, 1, =} How can I prove that L is not a regular language using pumping lemma and contradiction?
shallowfalcon
asked
in
Theory of Computation
Oct 17, 2022
by
shallowfalcon
421
views
theory-of-computation
pumping-lemma
regular-language
0
votes
1
answer
6
Self Doubt
$L=\{wa^nw^Rb^n\mid w\in \left \{ a,b \right \}^\ast ,n\geqslant 0\}$ Can anyone give me step by step solution that shows this is not CFL by pumping Lemma?
tusharb
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in
Theory of Computation
Jul 29, 2022
by
tusharb
474
views
self-doubt
theory-of-computation
pumping-lemma
1
vote
1
answer
7
identify language is regular or not L={wcw^r | w,c belongs to E*} E={a,b}
identify language is regular or not L={wcw^r | w,c belongs to E*} E={a,b} if yes then why please explain
sachin_27
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in
Theory of Computation
Jun 1, 2022
by
sachin_27
1.3k
views
theory-of-computation
regular-language
pumping-lemma
context-free-language
0
votes
1
answer
8
pumping length - TOC
What is meant by ‘pumping length’ and how can we find it?
atulcse
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in
Theory of Computation
Jan 28, 2022
by
atulcse
546
views
theory-of-computation
pumping-lemma
3
votes
2
answers
9
NIELIT 2017 OCT Scientific Assistant A (CS) - Section B: 12
The logic of pumping lemma is a good example of the pigeon-hole principle the divide and conquer technique recursion iteration
admin
asked
in
Theory of Computation
Apr 1, 2020
by
admin
920
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nielit2017oct-assistanta-cs
theory-of-computation
pumping-lemma
1
vote
0
answers
10
Peter Linz Edition 4 Exercise 8.1 Question 8 (Page No. 212)
Determine whether or not the following languages are context-free. (a) $L=$ {$a^nww^Ra^n : n ≥ 0, w ∈$ {$a,b$}*} (b) $L=$ {$a^nb^ja^nb^j : n ≥ 0, j ≥ 0$}. (C) $L=$ {$a^nb^ja^jb^n : n ≥ 0, j ≥ 0$}. (d) $L=$ {$a^nb^ja^kb^l : n + j ≤ k + l$ ... $ L=$ {$a^nb^nc^j : n ≤j$}. (g) $L=$ {$w ∈$ {$a, b, c$}* $: n_a(w)= n_b (w)=2n_c(w)$}.
Naveen Kumar 3
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in
Theory of Computation
Jun 25, 2019
by
Naveen Kumar 3
689
views
peter-linz
peter-linz-edition4
theory-of-computation
context-free-language
pumping-lemma
proof
2
votes
2
answers
11
Peter Linz Edition 4 Exercise 8.1 Question 5 (Page No. 212)
Is the language L = {$a^nb^m : n = 2^m$} context-free?
Naveen Kumar 3
asked
in
Theory of Computation
Jun 25, 2019
by
Naveen Kumar 3
553
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
context-free-language
1
vote
2
answers
12
Peter Linz Edition 4 Exercise 8.1 Question 1 (Page No. 212)
Show that the language $L=${$a^nb^nc^m,n\neq m$} is not context-free.
Naveen Kumar 3
asked
in
Theory of Computation
Jun 25, 2019
by
Naveen Kumar 3
479
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
context-free-language
0
votes
0
answers
13
Michael Sipser Edition 3 Exercise 2 Question 37 (Page No. 158)
Prove the following stronger form of the pumping lemma, where in both pieces $v$ and $y$ must be nonempty when the string $s$ is broken up$.$If $A$ is a context-free language, then there is a number $k$ where, if $s$ is any string in $A$ of ... $i\geq 0,uv^{i}xy^{i}z\in A,$ $v\neq\epsilon$ and $y\neq\epsilon,$and $\mid vxy\mid\leq k.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
509
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
1
vote
1
answer
14
Michael Sipser Edition 3 Exercise 2 Question 36 (Page No. 158)
Give an example of a language that is not context free but that acts like a $CFL$ in the pumping lemma$.$ Prove that your example works$.$ $\text{(See the analogous example for regular languages in Question 54.)}$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
1.7k
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
proof
1
vote
1
answer
15
Michael Sipser Edition 3 Exercise 2 Question 34 (Page No. 157)
Let $G = (V, \Sigma, R, S)$ be the following grammar. $V = \{S, T, U\}; \Sigma = \{0, \#\};$ and $R$ is the set of rules$:$ $S\rightarrow TT\mid U$ $T\rightarrow 0T\mid T0\mid \#$ ... existence of a pumping length $p$ for $B.$ What is the minimum value of $p$ that works in the pumping lemma$?$ Justify your answer$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
1.1k
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
proof
0
votes
1
answer
16
Michael Sipser Edition 3 Exercise 2 Question 30 (Page No. 157)
Use the pumping lemma to show that the following languages are not context free$.$ $\{0^{n}1^{n}0^{n}1^{n}\mid n\geq 0\}$ $\{0^{n}\#0^{2n}\#0^{3n}\mid n\geq 0\}$ $\{w\#t\mid w$ $\text{ is a substring of}$ $ t,$ $\text{where}$ ... $\text{each}$ $ t_{i}\in\{a,b\}^{*},$ $\text{and}$ $ t_{i}=t_{j}$ $\text{ for some}$ $ i\neq j\}$
admin
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in
Theory of Computation
May 4, 2019
by
admin
1.1k
views
michael-sipser
theory-of-computation
context-free-language
pumping-lemma
1
vote
1
answer
17
Michael Sipser Edition 3 Exercise 1 Question 55 (Page No. 91)
The pumping lemma says that every regular language has a pumping length $p,$ such that every string in the language can be pumped if it has length $p$ or more. If $p$ is a pumping length for language $A,$ so is any length $p^{'}\geq p.$ The minimum pumping ... $\epsilon$ $1^{*}01^{*}01^{*}$ $10(11^{*}0)^{*}0$ $1011$ $\sum^{*}$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
2.2k
views
michael-sipser
theory-of-computation
regular-language
pumping-lemma
proof
descriptive
0
votes
1
answer
18
Michael Sipser Edition 3 Exercise 1 Question 54 (Page No. 91)
Consider the language $F=\{a^{i}b^{j}c^{k}|i,j,k\geq 0$ $\text{and if}$ $ i = 1$ $\text{then} $ $ j=k\}.$ Show that $F$ is not regular. Show that $F$ acts like a regular language in the pumping lemma. ... three conditions of the pumping lemma for this value of $p.$ Explain why parts $(a)$ and $(b)$ do not contradict the pumping lemma.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
894
views
michael-sipser
theory-of-computation
finite-automata
regular-language
pumping-lemma
proof
descriptive
0
votes
1
answer
19
Michael Sipser Edition 3 Exercise 1 Question 30 (Page No. 88)
Describe the error in the following $ $proof$"$ that $0^{*}1^{*}$ is not a regular language. $($An error must exist because $0^{*}1^{*}$ is regular.$)$ The proof is by contradiction. Assume that $0^{*}1^{*}$ is regular ... example $1.73$ shows that $s$ cannot be pumped. Thus you have a contradiction. So $0^{*}1^{*}$ is not regular.
admin
asked
in
Theory of Computation
Apr 21, 2019
by
admin
889
views
michael-sipser
theory-of-computation
finite-automata
pumping-lemma
proof
1
vote
1
answer
20
Michael Sipser Edition 3 Exercise 1 Question 29 (Page No. 88)
Use the pumping lemma to show that the following languages are not regular. $A_{1}=\{0^{n}1^{n}2^{n}|n\geq 0\}$ $A_{2}=\{www|w\in\{a,b\}^{*}\}$ $A_{3}=\{a^{{2}^{n}}|n\geq 0\}$ $\text{(Here,}$\text{$a^{{2}^{n}}$}$ $\text{means a strings of $2^{n}$ a's.)}$
admin
asked
in
Theory of Computation
Apr 21, 2019
by
admin
2.8k
views
michael-sipser
theory-of-computation
finite-automata
regular-language
pumping-lemma
0
votes
1
answer
21
Self doubt:Pumping Lemma
How by Pumping Lemma we can prove that “context free grammar generate an infinite number of strings” and here what could be pumping length ?
srestha
asked
in
Theory of Computation
Apr 19, 2019
by
srestha
649
views
theory-of-computation
pumping-lemma
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