5. (15 points) Let f : NN be defined as 3a +1 f(x) = 1/2 I...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
5. (15 points) Let f : NN be defined as 3a +1 f(x) = 1/2 I is odd I is even %3D For every natural number a, if you start with z and iterate f, you obtain a sequence a, f(x), f(f(r)), fS(=))),.... Stop if you ever hit 1. For example, if r D 17, we get the sequence 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. It has been checked by computers that if we start with any number a < 1017, we will eventually hit 1 and terminate, but it is unknown whether this is true for every integer r. This is known as Collatz's conjecture'. Let R be an oracle for HALTTM. Construct an oracle Turing Machine MR such that MR accepts e if Collatz's conjecture is true (all numbers a hit 1 eventually), and rejects it if Collatz's conjecture is false (there is some r that does not hit 1). 5. (15 points) Let f : NN be defined as 3a +1 f(x) = 1/2 I is odd I is even %3D For every natural number a, if you start with z and iterate f, you obtain a sequence a, f(x), f(f(r)), fS(=))),.... Stop if you ever hit 1. For example, if r D 17, we get the sequence 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. It has been checked by computers that if we start with any number a < 1017, we will eventually hit 1 and terminate, but it is unknown whether this is true for every integer r. This is known as Collatz's conjecture'. Let R be an oracle for HALTTM. Construct an oracle Turing Machine MR such that MR accepts e if Collatz's conjecture is true (all numbers a hit 1 eventually), and rejects it if Collatz's conjecture is false (there is some r that does not hit 1).
Expert Answer:
Answer rating: 100% (QA)
as per the given question let consider the values ar... View the full answer
Related Book For
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
Posted Date:
Students also viewed these programming questions
-
Let for any natural number x. If you start with an integer x and iterate f, you obtain a sequence, x, f(x), f(f(x)), . . . . Stop if you ever hit 1. For example, if x = 17, you get the sequence 17,...
-
Use mathematical induction to prove that, for every natural number n,
-
Let f be an odd function and g be an even function and suppose that Use geometric reasoning to calculate each of the following (a) (b) (c) (d) (e) (f) Jo rods f(x) dx g(x) dx f(x)l dx -1 [-g(x)l dx...
-
31. Which combination of the compounds and their geometry are correct h) CIF, - V-shaped e) CIF, - Tshaped OB. a HeCl, - linoar 24. Which of the following havea bond angle smaller than tetrahodral...
-
Find the z value described and sketch the area described. Find z such that 6% of the standard normal curve lies to the left of z.
-
Two particles carrying charges \(q_{1}=-4 \mu \mathrm{C}\) and \(q_{2}=\) \(12 \mu \mathrm{C}\) are located \(5 \mathrm{~m}\) apart. Choose a coordinate system where the first particle is at the...
-
Two water jets of equal size and speed strike each other as shown in Fig. P5.57. Determine the speed, \(V\), and direction, \(\theta\), of the resulting combined jet. Gravity is negligible. Figure...
-
The following information is for Takin Enterprises Ltd. Instructions (a) Using the above information, prepare monthly income statements (as far as the data permit) in colunmar form for February,...
-
Product Cott has sales of $200,000, a contribution margin of 20%, and a margin of safety of $80,000. What is Cott's fixed cost? Snyder Co. manufactures fans with direct material costs of $10 per...
-
A pin is required for forming a linkage pivot. Find the dimensions required for a 50-mm basic size pin and clevis with a sliding fit.
-
A capacitor has a capacitance of 0.1 ?F and is charged to a voltage of 120 V. Calculate the energy stored in the capacitor.
-
What are the purposes of (a) the income statement, (b) the balance sheet, (c) the statement of cash flows, and (d) the statement of stockholders equity?
-
What can a financial analyst find in the MD&A section of the annual report?
-
Describe what is meant by deferred taxes. In which situation can it become a liability and when can it become an asset?
-
What is the eventual goal of the IASB?
-
Define goodwill. How is it recorded on the balance sheet?
-
An integer is 13 more than 3 times another. If the product of the two integers is then find the integers.
-
2. In the circuit given in Figure 2, i,(t) = 5.67cos(5t)A and v (t) = 70.71 cos(5t 60) V a) Find the equivalent load impedance. State whether the load is inductive or capacitive. b) Calculate the...
-
List all possible rational zeros. a. h(x) = 4x5 - 2x3 + 6x - 12 b. g(x) = 3x4 - x3 + 5x2 - x + 1 c. f(x) = x3 - 2x2 + x - 24
-
For the function f (x) = x4 + 8x3 + 5x2 - 38x + 24, Use long division to determine whether each of the following is a factor of f (x). a. x + 6 b. x + 1 c. x - 4
-
Find an equation of an ellipse satisfying the given conditions. a. Vertices: (-7, 0) and (7, 0); foci: (-3, 0) and (3, 0) b. Vertices: (0, -6) and (0, 6); foci: (0, -4) and (0, 4) c. Vertices: (0,...
-
Why is it important to pay attention to cultural differences when interviewing a client?
-
What does the term "unauthorized practice of law" mean, and how does it limit your relationship with a client?
-
Why is it important to acknowledge how a client is feeling at the initial interview?
Study smarter with the SolutionInn App