Computer Science: An Overview (13th Edition) (What's New in Computer Science)
13th Edition
ISBN: 9780134875460
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Chapter 12, Problem 14CRP
Program Plan Intro
Turing machine:
Turing machine is used as a tool to understand the power of
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(b) Suppose that you were asked to design a
Turing machine that, when started scan-
ning a square on a completely blank tape,
writes the string ababbaab on the tape
and halts scanning the leftmost symbol of
this string. What is the minimal number
of states required in order to accomplish
this?
a) Explain on Simulated Annealing algorithm behaves at very high temperatures,
and how it behaves at very low temperatures.
(b) Imagine the implementation of Simulated Annealing algorithm in real life. Let's
say, you have a caretaker at your home. Your home has a garden and it has a
fountain with a network of pipes that contains 150 faucets. You informed your
caretaker that you are going for short holiday to Langkawi for 3 days and when
you return you would like the fountain to spray as high as possible. Your
caretaker knows that it is impossible to check all faucets within 3 days to obtain
an optimal setting. You can use Simulated Annealing algorithm to maximize the
height of the fountain, also can assume whether a faucet can be ON or OFF and
measuring the water height. Adding to that, you can make any other
assumptions required for this scenario, explain clearly using Simulated Annealing
algorithm.
Given a transition graph of a Turing machine.
(a) Write a program for the Turing Machine Simulator based
on the given transition graph.
(b) Test (at least one time) your program (a) on the Turing
Machine Simulator.
Give the screen images:
- before the work of TMS
- after the work of TMS
(c) What the given Turing machine computes?
(d) In how many steps the given Turing machine processes
the input data of the length n?
Chapter 12 Solutions
Computer Science: An Overview (13th Edition) (What's New in Computer Science)
Ch. 12.1 - Prob. 1QECh. 12.1 - Prob. 2QECh. 12.1 - Prob. 3QECh. 12.1 - Prob. 4QECh. 12.2 - Prob. 1QECh. 12.2 - Prob. 2QECh. 12.2 - Prob. 3QECh. 12.2 - Prob. 4QECh. 12.2 - Prob. 5QECh. 12.3 - Prob. 1QE
Ch. 12.3 - Prob. 3QECh. 12.3 - Prob. 5QECh. 12.3 - Prob. 6QECh. 12.4 - Prob. 1QECh. 12.4 - Prob. 2QECh. 12.4 - Prob. 3QECh. 12.5 - Prob. 1QECh. 12.5 - Prob. 2QECh. 12.5 - Prob. 4QECh. 12.5 - Prob. 5QECh. 12.6 - Prob. 1QECh. 12.6 - Prob. 2QECh. 12.6 - Prob. 3QECh. 12.6 - Prob. 4QECh. 12 - Prob. 1CRPCh. 12 - Prob. 2CRPCh. 12 - Prob. 3CRPCh. 12 - In each of the following cases, write a program...Ch. 12 - Prob. 5CRPCh. 12 - Describe the function computed by the following...Ch. 12 - Describe the function computed by the following...Ch. 12 - Write a Bare Bones program that computes the...Ch. 12 - Prob. 9CRPCh. 12 - In this chapter we saw how the statement copy...Ch. 12 - Prob. 11CRPCh. 12 - Prob. 12CRPCh. 12 - Prob. 13CRPCh. 12 - Prob. 14CRPCh. 12 - Prob. 15CRPCh. 12 - Prob. 16CRPCh. 12 - Prob. 17CRPCh. 12 - Prob. 18CRPCh. 12 - Prob. 19CRPCh. 12 - Analyze the validity of the following pair of...Ch. 12 - Analyze the validity of the statement The cook on...Ch. 12 - Suppose you were in a country where each person...Ch. 12 - Prob. 23CRPCh. 12 - Prob. 24CRPCh. 12 - Suppose you needed to find out if anyone in a...Ch. 12 - Prob. 26CRPCh. 12 - Prob. 27CRPCh. 12 - Prob. 28CRPCh. 12 - Prob. 29CRPCh. 12 - Prob. 30CRPCh. 12 - Prob. 31CRPCh. 12 - Suppose a lottery is based on correctly picking...Ch. 12 - Is the following algorithm deterministic? Explain...Ch. 12 - Prob. 34CRPCh. 12 - Prob. 35CRPCh. 12 - Does the following algorithm have a polynomial or...Ch. 12 - Prob. 37CRPCh. 12 - Summarize the distinction between stating that a...Ch. 12 - Prob. 39CRPCh. 12 - Prob. 40CRPCh. 12 - Prob. 41CRPCh. 12 - Prob. 42CRPCh. 12 - Prob. 43CRPCh. 12 - Prob. 44CRPCh. 12 - Prob. 46CRPCh. 12 - Prob. 48CRPCh. 12 - Prob. 49CRPCh. 12 - Prob. 50CRPCh. 12 - Prob. 51CRPCh. 12 - Prob. 52CRPCh. 12 - Prob. 1SICh. 12 - Prob. 2SICh. 12 - Prob. 3SICh. 12 - Prob. 4SICh. 12 - Prob. 5SICh. 12 - Prob. 6SICh. 12 - Prob. 7SICh. 12 - Prob. 8SI
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- In "Computing Machines and Intelligence," the English mathematician Alan Turing (1912-1954) wrote, "If each man had a definite set of rules of conduct by which he regulated his life, he would be a machine, but there are no such rules, so men cannot be machines." Using what you now know about Logic, determine whether this statement make sense and explain. Construct a truth table for Turing's statement and determine if this statement is a tautology.arrow_forwardFor a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M) contains the set of all strings accepted by M. For a Turing machine M and an input x = {0,1}*, Steps(M, x) refers to the number of steps taken by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or right) of the tape head. For a Turing machine M and an input x = {0,1}*, we define the following: ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x} Informally, it contains all locations on the tape that are visited when M is ecuted on x. The leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so on. A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements such that π(w₁) = W2.arrow_forwardA common problem that arises in software maintenance is identifying (and then removing) dead code, code that will never be executed no matter what input the program is given. The analogous problem for TMs would be to determine if a state is never entered, no matter what input the TM is given. Prove by reduction that Ldead, the set of pairs (T,s) where T is a Turing machine and s is a dead state, is not recursive.arrow_forward
- 5arrow_forwardFor a Turing machine M, (M) refers to the binary representation of M. For a Turing machine M, L(M) contains the set of all strings accepted by M. For a Turing machine M and an input x € {0,1}*, Steps(M, x) refers to the number of steps taken by M to execute on x before it halts. Here, one step of execution of M on x = one movement (left or right) of the tape head. For a Turing machine M and an input x = {0,1}*, we define the following: ReachCells(M,x) = {i : M reaches ith tape cell when M is executed on x} Informally, it contains all locations on the tape that are visited when M is ecuted on x. The leftmost location on the tape is the first tape cell, the location next to it is the second tape cell, and so on. A string w₁ is an anagram of w2 if w₁ can be obtained by rearranging the alphabets of w2. Formally, if w₁ is an n length string, wê is called an anagram of w₁ if there exists a permutation à on n elements such that π(w₁) = W2.arrow_forwardOn an island, a group of people are living until a visitor arrives with an odd directive: everyone with blue eyes must leave the island as quickly as possible. Every evening, a flight will depart at 8:00. Everyone can see the colour of everyone else's eyes, but they are blind to their own (nor is anyone allowed to tell them). They also do not know the number of persons who have blue eyes, but they do know that at least one person has them. How long will it take the folks with blue eyes to leave?arrow_forward
- Source:https://www.mog.dog/files/SP2019/Sipser_Introduction.to.the.Theory.of.Computation.3E.pdfarrow_forwardDetermine and draw a matrix or a state machine of the Turing machine that computes the function: f(n) =4n+3 The machine should therefore start with a natural number n on the tape and stop with the number 4n 3 on the tape. Drawarrow_forwardHey, could you help me out with this problem? I'm having trouble figuring it out and would really appreciate a detailed, step-by-step explanation leading to the solution. question that I really need help with:5.13 A useless state in a Turing machine is one that is never entered on any input string. Consider the problem of determining whether a Turing machine has any useless states. Formulate this problem as a language and show that it is undecidable.arrow_forward
- Define the notion of a Turing machine with a two-dimensional tape. Show that a 2-tape ordinary Turing machine can simulate it. Estimate the efficiency of the above simulation. give the running time of the new machine with the running time function TM (n) of the original machine.arrow_forward1. Turing machines may also be used to compute functions. Give a state-transition diagram for a Turing machine that takes as input a binary string w, increments w, and enters the accepting state. For example, on input w = 100111, the Turing machine begins like this: 90 1|0|0|11|1|-|-|-|-|-|- The Turing machine should halt with 101000 on the tape: Jaccept 101000arrow_forwardDesign a Turing machine with no more than three states that accepts thelanguageL (a (a + b)∗).Assume that Σ = {a, b}. Is it possible to do this with a two-state machine?arrow_forward
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