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Recent questions tagged peter-linz-edition5
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Peter Linz Edition 5 Exercise 9.1 Question 7(a) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = L(aba^*b)$.
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = L(ab...
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Peter Linz Edition 5 Exercise 9.1 Question 6 (Page No. 238)
$\text{Example}:$ Design a Turing machine that copies strings of $1’s$. More precisely, find a machine that performs the computation $q_0q\vdash^*q_fww,$ for any $w\in\{1\}^+$. What happens in Example if the string $w$ contains any symbol other than $1?$
$\text{Example}:$ Design a Turing machine that copies strings of $1’s$. More precisely, find a machine that performs the computation ...
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Peter Linz Edition 5 Exercise 9.1 Question 5 (Page No. 238)
What language is accepted by the Turing machine whose transition graph is in the figure below$?$
What language is accepted by the Turing machine whose transition graph is in the figure below$?$
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Peter Linz Edition 5 Exercise 9.1 Question 4 (Page No. 238)
$\text{Example}:$ For $\Sigma = \{a,b\}$ design a Turing machine that accepts $L = \{a^nb^n:n\geq 1\}$. Is there any input for which the Turing machine in Example goes into an infinite loop$?$
$\text{Example}:$ For $\Sigma = \{a,b\}$ design a Turing machine that accepts $L = \{a^nb^n:...
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Peter Linz Edition 5 Exercise 9.1 Question 3 (Page No. 238)
$\text{Example}:$ For $\Sigma = \{a,b\}$ design a Turing machine that accepts $L = \{a^nb^n:n\geq 1\}$. Determine what the Turing machine in Example does when presented with the inputs $aba$ and $aaabbbb$.
$\text{Example}:$ For $\Sigma = \{a,b\}$ design a Turing machine that accepts $L = \{a^nb^n:...
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Peter Linz Edition 5 Exercise 9.1 Question 2 (Page No. 238)
Design a Turing machine with no more than three states that accept the language $L(a(a+b)^*)$. Assume that $\Sigma = \{a,b\}$. Is it possible to do this with a two-state machine$?$
Design a Turing machine with no more than three states that accept the language $L(a(a+b)^*)$. Assume that $\Sigma = \{a,b\}$. Is it possible to do this with a two-state ...
Rishi yadav
182
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Peter Linz Edition 5 Exercise 9.1 Question 1 (Page No. 238)
Write a Turing machine simulator in some higher-level programming language. Such a simulator should accept as input the description of any Turing machine, together with an initial configuration, and should produce as output the result of the computation.
Write a Turing machine simulator in some higher-level programming language. Such a simulator should accept as input the description of any Turing machine, together with a...
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 6,7 (Page No. 276)
$\text{Exercise}:6$ ... above exercise to show that any context-free language not containing $\lambda$ is accepted by some linear bounded automaton.
$\text{Exercise}:6$ Show that for every context-free language there exists an accepting pda, such that the number of symbols in the stack never exceeds the length of the...
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Peter Linz Edition 5 Exercise 10.5 Question 5 (Page No. 276)
$\text{Example}:$ Find a linear bounded automaton that accepts the language $L = \{a^{n!}:n\geq0\}$. Find a lba for the complement of the language in Example, assuming that $\Sigma = \{a,b\}$.
$\text{Example}:$ Find a linear bounded automaton that accepts the language $L = \{a^{n!}...
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 4(f) (Page No. 276)
Find linear bounded automata for the following languages. $L =\Big \{www^R:w\in \{a,b\}^+\Big\}$.
Find linear bounded automata for the following languages. $L =\Big \{www^R:w\in \{a,b\}^+\Big\}$.
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 4(e) (Page No. 276)
Find linear bounded automata for the following languages. $L = \Big\{w^n : w\in\{a,b\}^+,n\geq2\Big\}$.
Find linear bounded automata for the following languages. $L = \Big\{w^n : w\in\{a,b\}^+,n\geq2\Big\}$.
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 4(d) (Page No. 275)
Find linear bounded automata for the following language. $L = \Big\{ww:w\in\{a,b\}^+\Big\}$.
Find linear bounded automata for the following language. $L = \Big\{ww:w\in\{a,b\}^+\Big\}$.
Rishi yadav
429
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Apr 3, 2019
Theory of Computation
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Peter Linz Edition 5 Exercise 10.5 Question 4(c) (Page No. 275)
Find linear bounded automata for the following language. $L = \{a^n: \text{n is not a prime number}\}$.
Find linear bounded automata for the following language. $L = \{a^n: \text{n is not a prime number}\}$.
Rishi yadav
266
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Apr 3, 2019
Theory of Computation
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Peter Linz Edition 5 Exercise 10.5 Question 4(b) (Page No. 275)
Find linear bounded automata for the following language. $L = \{a^n: \text{n is a prime number}\}$.
Find linear bounded automata for the following language. $L = \{a^n: \text{n is a prime number}\}$.
Rishi yadav
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 4(a) (Page No. 275)
Find linear bounded automata for the following language. $L = \{a^n: n = m^2,m\geq 1\}$
Find linear bounded automata for the following language. $L = \{a^n: n = m^2,m\geq 1\}$
Rishi yadav
156
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 3 (Page No. 275)
Consider an offline Turing machine in which the input can be read only once, moving left to right, not rewritten. On its work tape, it can use at most n extra cells for work space, where n is fixed for all inputs. Show that such a machine is equivalent to a finite automaton.
Consider an offline Turing machine in which the input can be read only once, moving left to right, not rewritten. On its work tape, it can use at most n extra cells for w...
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Apr 3, 2019
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Peter Linz Edition 5 Exercise 10.5 Question 2 (Page No. 275)
$\text{Example: }$Find a linear bounded automaton that accepts the language $L = \{a^{n!}:n\geq0\}$ Find a solution for Example that does not require track as scratch space.
$\text{Example: }$Find a linear bounded automaton that accepts the language $L = \{a^{n!}:n\g...
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173
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Apr 2, 2019
Theory of Computation
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Peter Linz Edition 5 Exercise 10.5 Question 1 (Page No. 275)
$\text{Example: }$Find a linear bounded automaton that accepts the language $L = \{a^{n!}:n\geq0\}$ Give details for the solution of Example.
$\text{Example: }$Find a linear bounded automaton that accepts the language $L = \{a^{n!}:n\g...
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230
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Apr 2, 2019
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Peter Linz Edition 5 Exercise 10.4 Question 9 (Page No. 273)
Show that the Cartesian product of a finite number of countable sets is countable.
Show that the Cartesian product of a finite number of countable sets is countable.
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Peter Linz Edition 5 Exercise 10.4 Question 8 (Page No. 273)
Suppose that $S_1$ and $S_2$ are countable sets. Show that then $S_1\cup S_2$ and $S_1 \times S_2$ are also countable.
Suppose that $S_1$ and $S_2$ are countable sets. Show that then $S_1\cup S_2$ and $S_1 \times S_2$ are also countable.
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Peter Linz Edition 5 Exercise 10.4 Question 7 (Page No. 273)
Show that the set of all triplets, $(i,j,k)$ with $i,j,k$ positive integers, is countable,
Show that the set of all triplets, $(i,j,k)$ with $i,j,k$ positive integers, is countable,
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Apr 2, 2019
Theory of Computation
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Peter Linz Edition 5 Exercise 10.4 Question 5 (Page No. 272)
Design a Turing machine that enumerates the following set in proper order $L = \{a^nb^n:n\geq 1\}$.
Design a Turing machine that enumerates the following set in proper order $L = \{a^nb^n:n\geq 1\}$...
Rishi yadav
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Theory of Computation
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Peter Linz Edition 5 Exercise 10.4 Question 4 (Page No. 272)
$\text{Exercise 3:}$ Sketch a Turing machine program that enumerates the set {0,1}+{0,1}+ in proper order. $\text{Exercise 4:}$ What is the index of $0^i1^j$ in Exercise 3$?$
$\text{Exercise 3:}$ Sketch a Turing machine program that enumerates the set {0,1}+{0,1}+ in proper order.$\text{Exercise 4:}$ What is the index of $0^i1^j$ in Exercise 3...
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Peter Linz Edition 5 Exercise 10.4 Question 3 (Page No. 272)
Sketch a Turing machine program that enumerates the set $\{0,1\}^+$ in proper order.
Sketch a Turing machine program that enumerates the set $\{0,1\}^+$ in proper order.
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Peter Linz Edition 5 Exercise 10.4 Question 2 (Page No. 272)
Give a complete encoding, using the suggested method, for the Turing machine with $\delta(q_1,a_1) = (q_1,a_1,R)$, $\delta(q_1,a_2) = (q_3,a_1,L)$, $\delta(q_3,a_1) = (q_2,a_2,L)$,
Give a complete encoding, using the suggested method, for the Turing machine with $\delta(q_1,a_1) = (q_1,a_1,R)$...
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Peter Linz Edition 5 Exercise 10.4 Question 1 (Page No. 272)
Sketch an algorithm that examines a string in $\{0,1\}^+$ to determine whether or not it represents an encoded Turing machine.
Sketch an algorithm that examines a string in $\{0,1\}^+$ to determine whether or not it represents an encoded Turing machine.
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Apr 2, 2019
Theory of Computation
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Peter Linz Edition 5 Exercise 10.3 Question 7 (Page No. 268)
$\text{Definition:}$ A $\text{nondeterministic pushdown acceptor (npda)}$ is defined by the septuple $M = (Q,\Sigma,\Gamma,\delta,q_0,z,F)$ where $Q$ ... being pushed on these two stacks. Show that the class of two-stack automata is equivalent to the class of Turing machines.
$\text{Definition:}$ A $\text{nondeterministic pushdown acceptor (npda)}$ is defined by the septuple $M = (Q,\Sigm...
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Peter Linz Edition 5 Exercise 10.3 Question 6 (Page No. 268)
Design a nondeterministic Turing machine that accepts the language. $L = \{a^n: \text{n is not a prime number}\}$.
Design a nondeterministic Turing machine that accepts the language. $L = \{a^n: \text{n is not a prime number}\}$...
Rishi yadav
298
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Apr 2, 2019
Theory of Computation
peter-linz
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Peter Linz Edition 5 Exercise 10.3 Question 5 (Page No. 268)
Write a simple program for a nondeterministic Turing machine that accepts the language $L = \Big\{ xww^Ry:x,y,w\in\{a,b\}^+,|x|\geq |y|\Big\}$. How would you solve this problem deterministically$?$
Write a simple program for a nondeterministic Turing machine that accepts the language $L = \Big\{ xww^Ry:x,y,w\in\{a,b\...
Rishi yadav
118
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Apr 2, 2019
Theory of Computation
peter-linz
peter-linz-edition5
theory-of-computation
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Peter Linz Edition 5 Exercise 10.3 Question 4 (Page No. 268)
Outline how one would write a program for a nondeterministic Turing machine to accept the language $L=\{ww^Rw:w\in\{a,b\}^+\}$.
Outline how one would write a program for a nondeterministic Turing machine to accept the language $L=\{ww^Rw...
Rishi yadav
139
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Apr 2, 2019
Theory of Computation
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