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Recent questions tagged peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 5(d) (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. $L = \{a^nb^m : m = n^2,n\geq1\}.$
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 5(c) (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. $\text{The complement of the language in }L = \{ww^R\}.$
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Theory of Computation
Apr 9, 2019
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Rishi yadav
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 5(b) (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. $L = \{w_1w_2: w_1 \neq w_2: |w_1| = |w_2|\}.$
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Theory of Computation
Apr 9, 2019
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Rishi yadav
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 5(a) (Page No. 244)
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. $L = \{ww^R\}.$
Rishi yadav
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in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
191
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 4 (Page No. 244)
Use a block diagram to sketch the implementation of a function f defined for all $w_1,w_2,w_3\in \{1\}^+$ by $f(w_1,w_2,w_3) = i,$ where $i$ is such that $|w_i| = \text{max}(|w_1|,|w_2|,|w_3|)$ if no two $w’s$ have the same length, and $i=0$ otherwise.
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Theory of Computation
Apr 9, 2019
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Peter Linz Edition 5 Exercise 9.2 Question 3(d) (Page No. 244)
Using adders, subtracters, comparers, copies or multipliers, draw block diagrams for Turing machines that compute the functions for all positive integers $n$ $f(n) = n!,$
Rishi yadav
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Theory of Computation
Apr 9, 2019
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Rishi yadav
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 3(e) (Page No. 244)
Using adders, subtracters, comparers, copiers or multipliers, draw block diagrams for Turing machines that compute the functions for all positive integers $n$ $f(n) = n^{n!},$
Rishi yadav
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in
Theory of Computation
Apr 9, 2019
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Rishi yadav
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 3(c) (Page No. 244)
Using adders, subtracters, comparers, copies or multipliers, draw block diagrams for Turing machines that compute the functions for all positive integers $n$ $f(n) = 2^n,$
Rishi yadav
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Theory of Computation
Apr 9, 2019
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Rishi yadav
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 3(b) (Page No. 244)
Using adders, subtracters, comparers, copies or multipliers, draw block diagrams for Turing machines that compute the functions for all positive integers $n$ $f(n) = n^5,$
Rishi yadav
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in
Theory of Computation
Apr 9, 2019
by
Rishi yadav
209
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 3(a) (Page No. 244)
Using adders, subtracters, comparers, copies or multipliers, draw block diagrams for Turing machines that compute the functions for all positive integers $n$ $f(n) = n(n+1),$
Rishi yadav
asked
in
Theory of Computation
Apr 9, 2019
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Rishi yadav
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Peter Linz Edition 5 Exercise 9.2 Question 2 (Page No. 244)
Establish a convention for representing positive and negative integers in unary notation. With your convention, sketch the construction of a subtracter for computing $x-y.$
Rishi yadav
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in
Theory of Computation
Apr 9, 2019
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Rishi yadav
191
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peter-linz
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Peter Linz Edition 5 Exercise 9.2 Question 1 (Page No. 244)
$\text{Example}:$ Design a Turing machine that multiples two positive integers in unary notation. Write out the complete solution to Example.
Rishi yadav
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Theory of Computation
Apr 9, 2019
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Rishi yadav
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Peter Linz Edition 5 Exercise 9.1 Question 19 (Page No. 240)
You may have noticed that all the examples in these sections had only one final state. Is it generally true that for any Turing machine, there exists another one with only one final state that accepts the same language$?$
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Apr 9, 2019
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peter-linz
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Peter Linz Edition 5 Exercise 9.1 Question 18 (Page No. 240)
$\text{Example}:$ Given two positive integers $x$ and $y$, design a Turing machine that computes $x+y$. Sketch how Example could be solved if $x$ and $y$ were represented in decimal.
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Theory of Computation
Apr 6, 2019
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267
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peter-linz
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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
Rishi yadav
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Theory of Computation
Apr 6, 2019
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Rishi yadav
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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Rishi yadav
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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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Apr 6, 2019
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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258
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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Rishi yadav
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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363
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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Rishi yadav
360
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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876
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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peter-linz
peter-linz-edition5
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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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Apr 6, 2019
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281
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peter-linz
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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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Theory of Computation
Apr 6, 2019
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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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Apr 6, 2019
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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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Apr 6, 2019
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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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Apr 6, 2019
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peter-linz
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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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