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Recent questions tagged peter-linz
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241
Peter Linz Edition 5 Exercise 9.1 Question 7(g) (Page No. 239)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{a^nb^na^nb^n:n\geq0\}$.
Rishi yadav
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in
Theory of Computation
Apr 6, 2019
by
Rishi yadav
226
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peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
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0
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242
Peter Linz Edition 5 Exercise 9.1 Question 7(f) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{a^nb^ma^{n+m}:n\geq0,m\geq1\}$.
Rishi yadav
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in
Theory of Computation
Apr 6, 2019
by
Rishi yadav
159
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peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
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243
Peter Linz Edition 5 Exercise 9.1 Question 7(e) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$ $L = \{w:n_a(w) = n_b(w)\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 6, 2019
by
Rishi yadav
195
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
0
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244
Peter Linz Edition 5 Exercise 9.1 Question 7(d) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{a^nb^m:n\geq1,n\neq m\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 6, 2019
by
Rishi yadav
135
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
0
votes
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245
Peter Linz Edition 5 Exercise 9.1 Question 7(c) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{w:|w| \text{ is a multiple of 3}\}$.
Rishi yadav
asked
in
Theory of Computation
Apr 6, 2019
by
Rishi yadav
242
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
0
votes
0
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246
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
264
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
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0
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247
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
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0
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248
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
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249
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
241
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
250
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
251
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
0
votes
0
answers
252
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
294
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
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answers
253
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
282
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
254
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
224
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
255
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
155
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
256
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
149
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
257
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
asked
in
Theory of Computation
Apr 5, 2019
by
Naveen Kumar 3
202
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
1
answer
258
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
asked
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
259
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
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
189
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
260
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
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261
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
262
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
263
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
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
264
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
191
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
0
answers
265
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
266
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
267
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
268
Peter Linz Edition 4 Exercise 4.1 Question 4 (Page No. 109)
Theorem 4.3 Let h be a homomorphism. If L is a regular language, then its homomorphic image h (L) is also regular. The family of regular languages is therefore closed under arbitrary homomorphisms. Proof: Let L be a regular language denoted by some ... 3, show that $h (r)$ is a regular expression. Then show that $h (r)$ denotes $h (L)$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
407
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
regular-expression
0
votes
0
answers
269
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
asked
in
Theory of Computation
Apr 4, 2019
by
Naveen Kumar 3
147
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
closure-property
0
votes
1
answer
270
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
asked
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
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