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Recent questions tagged regular-language
4
votes
4
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121
CMI2018-A-1
Which of the words below matches the regular expression $a(a+b)^{\ast}b+b(a+b)^{\ast}a$? $aba$ $bab$ $abba$ $aabb$
gatecse
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in
Theory of Computation
Sep 13, 2019
by
gatecse
1.0k
views
cmi2018
regular-language
regular-expression
easy
0
votes
0
answers
122
Ullman (TOC) Edition 3 Exercise 9.5 Question 2 (Page No. 418)
Show that the language $\overline{L_A}\cup \overline{L_B}$ is a regular language if and only if it is the set of all strings over its alphabet;i.e., if and only if the instance $(A,B)$ of PCP has no ... homomorphism, complementation and the pumping lemma for regular sets to show that $\overline{L_A}\cup \overline{L_B}$ is not regular.
admin
asked
in
Theory of Computation
Jul 26, 2019
by
admin
408
views
ullman
theory-of-computation
regular-language
pcp
descriptive
5
votes
3
answers
123
MadeEasy Test Series: Theory Of Computation - Regular Languages
Consider the following statements: $S_1:\{(a^n)^m|n\leq m\geq0\}$ $S_2:\{a^nb^n|n\geq 1\} \cup \{a^nb^m|n \geq1,m \geq 1\} $ Which of the following is regular? $S_1$ only $S_2$ only Both Neither of the above
Hirak
asked
in
Theory of Computation
May 25, 2019
by
Hirak
1.8k
views
made-easy-test-series
theory-of-computation
regular-language
0
votes
1
answer
124
self doubt: TOC
is union of regular language and context free language always regular?
Hirak
asked
in
Theory of Computation
May 22, 2019
by
Hirak
570
views
theory-of-computation
regular-language
context-free-language
3
votes
1
answer
125
Self Doubt : Ambiguity
Why is ambiguity in regular language is decidable and not decidable in CFL ? Can you give Example?
logan1x
asked
in
Theory of Computation
May 10, 2019
by
logan1x
1.2k
views
theory-of-computation
finite-automata
ambiguous
regular-language
context-free-language
context
0
votes
0
answers
126
Michael Sipser Edition 3 Exercise 2 Question 20 (Page No. 156)
Let $A/B = \{w\mid wx\in A$ $\text{for some}$ $x \in B\}.$ Show that if $A$ is context free and $B$ is regular$,$ then $A/B$ is context free$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
344
views
michael-sipser
theory-of-computation
context-free-language
regular-language
1
vote
1
answer
127
Michael Sipser Edition 3 Exercise 2 Question 18 (Page No. 156)
Let $C$ be a context-free language and $R$ be a regular language$.$ Prove that the language $C\cap R$ is context-free. Let $A = \{w\mid w\in \{a, b, c\}^{*}$ $\text{and}$ $w$ $\text{contains equal numbers of}$ $a’s, b’s,$ $\text{and}$ $c’s\}.$ Use $\text{part (a)}$ to show that $A$ is not a CFL$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
335
views
michael-sipser
theory-of-computation
context-free-language
regular-language
0
votes
0
answers
128
Michael Sipser Edition 3 Exercise 2 Question 17 (Page No. 156)
Use the results of $\text{Question 16}$ to give another proof that every regular language is context free$,$ by showing how to convert a regular expression directly to an equivalent context-free grammar$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
294
views
michael-sipser
theory-of-computation
regular-language
context-free-language
0
votes
1
answer
129
Michael Sipser Edition 3 Exercise 2 Question 13 (Page No. 156)
Let $G = (V, \Sigma, R, S)$ be the following grammar. $V = \{S, T, U\}; \Sigma = \{0, \#\};$ and $R$ is the set of rules$:$ $S\rightarrow TT\mid U$ $T\rightarrow 0T\mid T0\mid \#$ $U\rightarrow 0U00\mid\#$ Describe $L(G)$ in English. Prove that $L(G)$ is not regular$.$
admin
asked
in
Theory of Computation
May 4, 2019
by
admin
460
views
michael-sipser
theory-of-computation
context-free-grammar
regular-language
0
votes
0
answers
130
Michael Sipser Edition 3 Exercise 1 Question 72 (Page No. 93)
Let $M_{1}$ and $M_{2}$ be $\text{DFA's}$ that have $k_{1}$ and $k_{2}$ states, respectively, and then let $U = L(M_{1})\cup L(M_{2}).$ Show that if $U\neq\phi$ then $U$ contains some string $s,$ where $|s| < max(k1, k2).$ Show that if $U\neq\sum^{*},$ then $U$ excludes some string $s,$ where $|s| < k1k2.$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
323
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
2
votes
2
answers
131
Michael Sipser Edition 3 Exercise 1 Question 71 (Page No. 93)
Let $\sum = \{0,1\}$ Let $A=\{0^{k}u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$ Show that $A$ is regular. Let $B=\{0^{k}1u0^{k}|k\geq 1$ $\text{and}$ $u\in \sum^{*}\}.$Show that $B$ is not regular.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
500
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
0
votes
1
answer
132
Michael Sipser Edition 3 Exercise 1 Question 70 (Page No. 93)
We define the $\text{avoids}$ operation for languages $A$ and $B$ to be $\text{A avoids B = {w| w ∈ A and w doesn’t contain any string in B as a substring}.}$ Prove that the class of regular languages is closed under the ${avoids}$ operation.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
488
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
0
votes
0
answers
133
Michael Sipser Edition 3 Exercise 1 Question 68 (Page No. 93)
In the traditional method for cutting a deck of playing cards, the deck is arbitrarily split two parts, which are exchanged beforereassembling the deck. In a more complex cut, called $\text{Scarne's cut,}$ the deck is broken into three parts ... $ CUT(CUT(B)).}$ Show that the class of regular languages is closed under $\text{CUT}.$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
523
views
michael-sipser
theory-of-computation
regular-language
scarnes-cut
proof
descriptive
0
votes
0
answers
134
Michael Sipser Edition 3 Exercise 1 Question 67 (Page No. 93)
Let the rotational closure of language $A$ be $RC(A) = \{yx| xy ∈ A\}.$ Show that for any language $A,$ we have $RC(A) = RC(RC(A)).$ Show that the class of regular languages is closed under rotational closure.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
409
views
michael-sipser
theory-of-computation
regular-language
rotational-closure-of-language
descriptive
0
votes
0
answers
135
Michael Sipser Edition 3 Exercise 1 Question 63 (Page No. 92)
Let $A$ be an infinite regular language. Prove that $A$ can be split into two infinite disjoint regular subsets. Let $B$ and $D$ be two languages. Write $B\subseteqq D$ if $B\subseteq D$ and $D$ contains infinitely many ... regular languages where $B\subseteqq D,$ then we can find a regular language $C$ where $B\subseteqq C\subseteqq D.$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
348
views
michael-sipser
theory-of-computation
finite-automata
regular-language
descriptive
0
votes
0
answers
136
Michael Sipser Edition 3 Exercise 1 Question 58 (Page No. 92)
If $A$ is any language,let $A_{\frac{1}{2}-\frac{1}{3}}$ be the set of all strings in $A$ with their ,middle thirds removed so that $A_{\frac{1}{2}-\frac{1}{3}}=\{\text{xz|for some y,|x|=|y|=|z| and xyz $\in$ A\}}.$ Show that if $A$ is regular,then $A_{\frac{1}{2}-\frac{1}{3}}$ is not necessarily regular.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
221
views
michael-sipser
theory-of-computation
regular-language
proof
descriptive
0
votes
0
answers
137
Michael Sipser Edition 3 Exercise 1 Question 57 (Page No. 92)
If $A$ is any language,let $A_{\frac{1}{2}-}$ be the set of all first halves of strings in $A$ so that $A_{\frac{1}{2}-}=\{\text{x|for some y,|x|=|y| and xy $\in$ A\}}.$ Show that if $A$ is regular,then so is $A_{\frac{1}{2}-}.$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
264
views
michael-sipser
theory-of-computation
regular-language
proof
descriptive
0
votes
0
answers
138
Michael Sipser Edition 3 Exercise 1 Question 56 (Page No. 91)
If $A$ is a set of natural numbers and $k$ is a natural number greater than $1,$ let $B_{k}(A)=\{\text{w| w is the representation in base k of some number in A\}}.$ Here, we do not allow leading $0's$ in the representation ... a set $A$ for which $B_{2}(A)$ is regular but $B_{3}(A)$ is not regular$.$ Prove that your example works.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
333
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
1
vote
1
answer
139
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
140
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
921
views
michael-sipser
theory-of-computation
finite-automata
regular-language
pumping-lemma
proof
descriptive
0
votes
0
answers
141
Michael Sipser Edition 3 Exercise 1 Question 53 (Page No. 91)
Let $\sum=\{0,1,+,=\}$ and $ADD=\{x=y+z|x,y,z$ $\text{are binary integers,and}$ $x$ $\text{is the sum of}$ $y$ $\text{and}$ $z\}.$ Show that $\text{ADD}$ is not a regular.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
289
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
0
votes
1
answer
142
Michael Sipser Edition 3 Exercise 1 Question 49 (Page No. 90)
Let $B=\{1^{k}y|y\in\{0,1\}^{*}$ $\text{ and y contains at least}$ $k$ $1's,$ $\text{for every}$ $k\geq 1\}.$ Show that $B$ is a regular language. Let $C=\{1^{k}y|y\in\{0,1\}^{*}$ $\text{ and y contains at most}$ $k$ $1's,$ $\text{for every}$ $k\geq 1\}.$ Show that $C$ isn’t a regular language.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
433
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
1
vote
0
answers
143
Michael Sipser Edition 3 Exercise 1 Question 48 (Page No. 90)
Let $\sum = \{0,1\}$ and let $D = \{w|w$ $\text{contains an equal number of occurrences of the sub strings 01 and 10}\}.$ Thus $101\in D$ because $101$ contains a single $01$ and a single $10,$ but $1010\notin D$ because $1010$ contains two $10's$ and one $01.$ Show that $D$ is a regular language.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
255
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
0
votes
0
answers
144
Michael Sipser Edition 3 Exercise 1 Question 47 (Page No. 90)
Let $\sum=\{1,\#\}$ and let $Y=\{w|w=x_{1}\#x_{2}\#...\#x_{k}$ $\text{for}$ $k\geq 0,$ $\text{each}$ $ x_{i}\in 1^{*},$ $\text{and}$ $x_{i}\neq x_{j}$ $\text{for}$ $i\neq j\}.$ Prove that $Y$ is not regular.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
317
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
0
votes
0
answers
145
Michael Sipser Edition 3 Exercise 1 Question 46 (Page No. 90)
Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection,and complement. $\{0^{n}1^{m}0^{n}|m,n\geq 0\}$ $\{0^{m}1^{n}|m\neq n\}$ $\{w|w\in\{0,1\}^{*} \text{is not a palindrome}\}$ $\{wtw|w,t\in\{0,1\}^{+}\}$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
493
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
0
votes
0
answers
146
Michael Sipser Edition 3 Exercise 1 Question 45 (Page No. 90)
Let $\text{A/B = {w| wx ∈ A for some x ∈ B}}.$ Show that if $A$ is regular and $B$ is any language, then $\text{A/B}$ is regular.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
210
views
michael-sipser
theory-of-computation
finite-automata
regular-language
descriptive
0
votes
0
answers
147
Michael Sipser Edition 3 Exercise 1 Question 44 (Page No. 90)
Let $B$ and $C$ be languages over $\sum = \{0, 1\}.$ Define $B\overset{1}{\leftarrow} C = \{w\in B|$ $\text{for some}$ $y\in C$, $\text{strings}$ $w$ $\text{and}$ $y$ $\text{contain equal numbers of}$ $1’s\}.$ Show that the class of regular languages is closed under the $\overset{1}{\leftarrow}$operation.
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
213
views
michael-sipser
theory-of-computation
finite-automata
regular-language
descriptive
0
votes
0
answers
148
Michael Sipser Edition 3 Exercise 1 Question 43 (Page No. 90)
Let $A$ be any language. Define $\text{DROP-OUT(A)}$ to be the language containing all strings that can be obtained by removing one symbol from a string in $A.$ ... $\text{Theorem 1.47.}$
admin
asked
in
Theory of Computation
Apr 30, 2019
by
admin
666
views
michael-sipser
theory-of-computation
finite-automata
regular-language
proof
descriptive
0
votes
0
answers
149
Michael Sipser Edition 3 Exercise 1 Question 42 (Page No. 89)
For languages $A$ and $B,$ let the $\text{shuffle}$ of $A$ and $B$ be the language $\{w| w = a_{1}b_{1} \ldots a_{k}b_{k},$ where $ a_{1} · · · a_{k} ∈ A $ and $b_{1} · · · b_{k} ∈ B,$ each $a_{i}, b_{i} ∈ Σ^{*}\}.$ Show that the class of regular languages is closed under shuffle.
admin
asked
in
Theory of Computation
Apr 28, 2019
by
admin
334
views
michael-sipser
theory-of-computation
finite-automata
regular-language
0
votes
0
answers
150
Michael Sipser Edition 3 Exercise 1 Question 41 (Page No. 89)
For languages $A$ and $B,$ let the $\text{perfect shuffle}$ of $A$ and $B$ be the language $\text{{$w| w = a_{1}b_{1} · · · a_{k}b_{k},$ where $a_{1} · · · a_{k} ∈ A$ and $b_{1} · · · b_{k} ∈ B,$ each $a_{i}, b_{i} ∈ Σ$}}.$ Show that the class of regular languages is closed under perfect shuffle.
admin
asked
in
Theory of Computation
Apr 28, 2019
by
admin
457
views
michael-sipser
theory-of-computation
finite-automata
regular-language
perfect-shuffle
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