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Turing Machine Notes
Recent questions tagged turing-machine
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151
Peter Linz Edition 5 Exercise 9.1 Question 17 (Page No. 239)
$\text{Example}:$ Given two positive integers $x$ and $y,$ design a Turing machine that computes $x+y$. Suppose that in Example we had decided to represent $x$ and $y$ in binary. Write a Turing machine program for doing the indicated computation in this representation
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Peter Linz Edition 5 Exercise 9.1 Question 16 (Page No. 239)
$\text{Example}:$ Let $x$ and $y$ be two positive integers represented in unary notation. Construct a Turing machine that will halt in a final state $q_y$ if $x\geq y,$ and that will halt in a nonfinal state $q_n$ if $x < y.$ More ... $q_0w(x)0w(y) \vdash^* q_nw(x)0w(y)$ if $x < y$, Complete all the details in Example
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Peter Linz Edition 5 Exercise 9.1 Question 15 (Page No. 239)
$\text{Example}:$ Design a Turing machine that copies strings of $1’s$. More precisely, find a machine that performs the computation $q_0w \vdash^* q_fww,$ for any $w\in\{1\}^+$. Give convincing arguments that the Turing machine in Example does in fact carry out the indicated computation$.$
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Peter Linz Edition 5 Exercise 9.1 Question 14 (Page No. 239
$\text{Example}:$ Design a Turing machine that copies strings of $1's$. More precisely, find a machine that performs the computation $q_0w \vdash^* q_fww,$ for any $w\in\{1\}^+$. Give the sequence of instantaneous ... through when presented with the input $111$. What happens when this machine is started with $110$ on its tape$?$
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Peter Linz Edition 5 Exercise 9.1 Question 13 (Page No. 239)
$\text{Example}:$ Design a Turing machine that accepts $L = \{a^nb^nc^n:n\geq 1\}$. Write out a complete solution for Example.
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Peter Linz Edition 5 Exercise 9.1 Question 12 (Page No. 239)
Design a Turing machine $\Gamma = \{0,1,\square\}$ that, when started on any cell containing a blank or $a\space 1$, will halt if and only if its tape has a $0$ somewhere it.
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Peter Linz Edition 5 Exercise 9.1 Question 11(f) (Page No. 239)
Design Turing machines to compute the following functions for $x$ and $y$ positive integers represented in unary. $f(x) = \lfloor{\frac{x}{2}}\rfloor,$ where $\lfloor{\frac{x}{2}}\rfloor,$ denotes the largest integer less than or equal to $\frac{x}{2}.$
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Peter Linz Edition 5 Exercise 9.1 Question 11(e) (Page No. 239)
Design Turing machines to compute the following functions for $x$ and $y$ positive integers represented in unary. $f(x) = x \text { mod } 5. $
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Peter Linz Edition 5 Exercise 9.1 Question 11(d) (Page No. 239)
Design Turing machines to compute the following functions for $x$ and $y$ positive integers represented in unary $f(x) =\frac{x}{2},$ if $x$ is even, $ = \frac{x+1}{2},$ if $x$ is odd.
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Peter Linz Edition 5 Exercise 9.1 Question 11(c) (Page No. 239)
Design Turing machines to compute the following functions for $x$ and $y$ positive integers represented in unary $f(x,y) = 2x+3y$.
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Apr 6, 2019
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Peter Linz Edition 5 Exercise 9.1 Question 11(b) (Page No. 239)
Design Turing machines to compute the following functions for $x$ and $y$ positive integers represented in unary. $f(x,y) = x-y,$ $x>y,$ $= 0,$ $x\leq y$.
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Peter Linz Edition 5 Exercise 9.1 Question 11(a) (Page No. 239)
Design Turing machines to compute the following functions for $x$ and $y$ positive integers represented in unary. $f(x) = 3x$
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Peter Linz Edition 5 Exercise 9.1 Question 10 (Page No. 239)
Design a Turing machine that finds the middle of a string of even length. Specifically, if $w = a_1a_2...a_na_{n+1}...a_{2n},$ with $a_i\in\Sigma,$ the Turing machine should produce $\widehat{w} = a_1a_2...a_nca_{n+1}...a_{2n},$ where $c\in\Gamma-\Sigma$.
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Peter Linz Edition 5 Exercise 9.1 Question 9 (Page No. 239)
Construct a Turing machine to compute the function $f(w) = w^R$, where $w\in \{0,1\}^+$.
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Peter Linz Edition 5 Exercise 9.1 Question 8 (Page No. 239)
Design a Turing machine that accepts the language. $L = \Big\{ww:w\in \{a,b\}^+\Big\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(h) (Page No. 239)
Construct Turing machines that will accept the following languages on $\{a,b\}$ $L = \{a^nb^{2n}:n\geq 0\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(g) (Page No. 239)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{a^nb^na^nb^n:n\geq0\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(f) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{a^nb^ma^{n+m}:n\geq0,m\geq1\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(e) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$ $L = \{w:n_a(w) = n_b(w)\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(d) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{a^nb^m:n\geq1,n\neq m\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(c) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$. $L = \{w:|w| \text{ is a multiple of 3}\}$.
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Peter Linz Edition 5 Exercise 9.1 Question 7(b) (Page No. 238)
Construct Turing machines that will accept the following languages on $\{a,b\}$ $L = \{w:|w| \text{ is even }\}$.
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Theory of Computation
Apr 3, 2019
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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 $\{a,b\}$. $L = L(aba^*b)$.
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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 $1?$
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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$?$
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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$?$
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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 $aaabbbb$.
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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$?$
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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.
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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.
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