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Recent questions tagged peter-linz
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181
Peter Linz Edition 4 Exercise 4.3 Question 12 (Page No. 123)
Apply the pumping lemma to show that $L=$ {$a^nb^kc^{n+k}:n\geq0,k\geq0$} is not regular.
Naveen Kumar 3
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Theory of Computation
Apr 11, 2019
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Naveen Kumar 3
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peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
2
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0
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182
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
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Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
245
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peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
closure-property
0
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183
Peter Linz Edition 4 Exercise 4.3 Question 9 (Page No. 123)
Is the language $L=$ {$w∈$ {$a,b,c$}$^*$ $:|w|=3n_a(w)$} regular?
Naveen Kumar 3
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Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
284
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peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
0
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1
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184
Peter Linz Edition 4 Exercise 4.3 Question 8 (Page No. 123)
Show that the language $L=$ {$a^nb^{n+k}:n\geq0,k\geq1$} $\cup$ {$a^{n+k}b^n:n\geq0,k\geq3$} is not regular.
Naveen Kumar 3
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in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
286
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peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
1
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0
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185
Peter Linz Edition 4 Exercise 4.3 Question 7 (Page No. 123)
Show that the language $L=$ {$a^nb^n:n\geq0$} $\cup$ {$a^nb^{n+1}:n\geq0$} $\cup$ {$a^nb^{n+2}:n\geq0$} is not regular.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
153
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
1
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0
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186
Peter Linz Edition 4 Exercise 4.3 Question 5 (Page No. 122)
Determine whether or not the following languages on $Σ =$ {$a$} are regular. (a) $L =$ {$a^n: n ≥ 2,$ is a prime number}. (b) $L =$ {$a^n: n$ is not a prime number}. (c) $L =$ {$a^n: n = k^3$ for some $k ≥ 0$}. ( ... {$a^n: n$ is either prime or the product of two or more prime numbers}. (g) $L^*$, where $L$ is the language in part $(a)$.
Naveen Kumar 3
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in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
353
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peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
0
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0
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187
Peter Linz Edition 4 Exercise 4.3 Question 4 (Page No. 122)
Prove that the following languages are not regular. (a) $L =$ {$a^nb^la^k : k ≥ n + l$}. (b) $L =$ {$a^nb^la^k : k ≠ n + l$}. (c) $L =$ {$a^nb^la^k: n = l$ or $l ≠ k$}. (d) $L =$ {$a^nb^l : n ≤ l$}. (e) $L =$ {$w: n_a (w) ≠ n_b (w)$ }. (f) $L =$ {$ww : w ∈${$a, b$}$^*$}. (g) $L =$ {$wwww^R : w ∈$ {$a, b$}$^*$}.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
219
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
0
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1
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188
Peter Linz Edition 4 Exercise 4.3 Question 3 (Page No. 122)
Show that the language $L = \{w : n_a (w) = n_b(w) \}$ is not regular. Is $L^*$ regular?
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
334
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
regular-language
0
votes
0
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189
Peter Linz Edition 4 Exercise 4.3 Question 2 (Page No. 122)
Prove the following generalization of the pumping lemma. If $L$ is regular, then there exists an $m$, such that the following holds for every sufficiently long $w ∈ L$ and every one of its decompositions $w = u_1υu_2$, with $u_1,u_2 ∈ Σ^*, |υ| \geq m.$ The ... $|xy| ≤ m, |y| ≥ 1,$ such that $u_1xy^izu_2 ∈ L$ for all $i = 0,1, 2, .$
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
137
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peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
1
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1
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190
Peter Linz Edition 4 Exercise 4.3 Question 1 (Page No. 122)
Prove the following version of the pumping lemma. If $L$ is regular, then there is an $m$ such that, every $w ∈ L$ of length greater than $m$ can be decomposed as $w = xyz,$ with $|yz| ≤ m$ and $|y| ≥ 1,$ such that $xy^iz$ is in $L$ for all $i$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 11, 2019
by
Naveen Kumar 3
258
views
peter-linz
peter-linz-edition4
theory-of-computation
pumping-lemma
0
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191
Peter Linz Edition 4 Exercise 4.2 Question 15 (Page No. 114)
Describe an algorithm which, when given a regular grammar $G$, can tell us whether or not $L (G) = Σ^*$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
137
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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1
answer
192
Peter Linz Edition 4 Exercise 4.2 Question 14 (Page No. 114)
Find an algorithm for determining whether a regular language $L$ contains an infinite number of even-length strings.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
360
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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0
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193
Peter Linz Edition 4 Exercise 4.2 Question 13 (Page No. 114)
Show that there exists an algorithm that can determine for every regular language $L$, whether or not $|L| ≥ 5$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
127
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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194
Peter Linz Edition 4 Exercise 4.2 Question 12 (Page No. 113)
Let $L$ be any regular language on $Σ =$ {$a, b$}. Show that an algorithm exists for determining if $L$ contains any strings of even length.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
178
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peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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195
Peter Linz Edition 4 Exercise 4.2 Question 11 (Page No. 113)
The operation $tail (L)$ is defined as $tail(L)=$ {$v:uv∈L,u,v∈Σ^*$}. Show that there is an algorithm for determining whether or not $L = tail (L)$ for any regular $L$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
129
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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0
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196
Peter Linz Edition 4 Exercise 4.2 Question 10 (Page No. 113)
Show that there is an algorithm to determine if $L = shuffle (L, L)$ for any regular $L$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
174
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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197
Peter Linz Edition 4 Exercise 4.2 Question 9 (Page No. 113)
Let $L$ be a regular language on $Σ$ and $\widehat{w}$ be any string in $Σ^*$. Find an algorithm to determine if $L$ contains any $w$ such that $\widehat{w}$ is a substring of it, that is, such that $w = u\widehat{w} υ$ with $u,υ ∈Σ^*$ .
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
151
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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0
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198
Peter Linz Edition 4 Exercise 4.2 Question 8 (Page No. 113)
Exhibit an algorithm that, given any regular language $L$, determines whether or not $L =L^*$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
159
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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0
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199
Peter Linz Edition 4 Exercise 4.2 Question 7 (Page No. 113)
Exhibit an algorithm that, given any three regular languages, $L, L_1, L_2,$ determines whether or not $L = L_1 L_ 2$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
114
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
votes
0
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200
Peter Linz Edition 4 Exercise 4.2 Question 6 (Page No. 113)
Exhibit an algorithm for determining whether or not a regular language $L$ contains any string $w$ such that $w^ R ∈ L$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
128
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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1
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201
Peter Linz Edition 4 Exercise 4.2 Question 5 (Page No. 113)
A language is said to be a palindrome language if $L = L^R$. Find an algorithm for determining if a given regular language is a palindrome language.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
446
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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0
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202
Peter Linz Edition 4 Exercise 4.2 Question 4 (Page No. 113)
Show that for any regular $L_1$ and $L_2$ there is an algorithm to determine whether or not $L_1 = L_1/L_2$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
120
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
votes
0
answers
203
Peter Linz Edition 4 Exercise 4.2 Question 3 (Page No. 113)
Show that there exists an algorithm for determining if $λ ∈ L$, for any regular language $L$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
131
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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204
Peter Linz Edition 4 Exercise 4.2 Question 2 (Page No. 113)
Show that there exists an algorithm for determining if $L_1 ⊆ L_2$, for any regular languages $L_1$ and $L_2$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
162
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
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205
Peter Linz Edition 4 Exercise 4.2 Question 1 (Page No. 113)
Show that there exists an algorithm to determine whether or not $w ∈ L_1 − L_2$, for any given $w$ and any regular languages $L_1$ and $L_2$.
Naveen Kumar 3
asked
in
Theory of Computation
Apr 10, 2019
by
Naveen Kumar 3
253
views
peter-linz
peter-linz-edition4
theory-of-computation
regular-language
0
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206
Peter Linz Edition 5 Exercise 9.3 Question 1 (Page No. 248)
Consider the set of machine language instructions for a computer of your choice. Sketch how the various instructions in this set could be carried out by a Turing machine.
Rishi yadav
asked
in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
198
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
difficult
0
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207
Peter Linz Edition 5 Exercise 9.2 Question 8,9,10 (Page No. 245)
$\text{Exercise 8}:$ Give an implementation of the macroinstruction $\text{searchright} (a,q_i,q_j),$ ... $a$ by a blank. If the input contains no $a$, replace the rightmost nonblank symbol by a $b.$
Rishi yadav
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in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
390
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
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208
Peter Linz Edition 5 Exercise 9.2 Question 7 (Page No. 245)
Sketch the construction of a Turing machine that can perform the addition and multiplication of positive integers $x$ and $y$ given in the usual decimal notation.
Rishi yadav
asked
in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
176
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
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votes
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209
Peter Linz Edition 5 Exercise 9.2 Question 6 (Page No. 245)
Suggest a method for representing rational numbers on a Turing machine, then sketch a method for adding and subtracting such numbers.
Rishi yadav
asked
in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
232
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
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Peter Linz Edition 5 Exercise 9.2 Question 5(e) (Page No. 245)
Provide a “high-level” description for Turing machines that accept the following languages on $\{a,b\}.$ For each problem, define a set of appropriate macroinstructions that you feel are reasonably easy to implement. Then use them for the solution. $L = \{a^n : n\text{ is a prime number}\}.$
Rishi yadav
asked
in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
212
views
peter-linz
peter-linz-edition5
theory-of-computation
turing-machine
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