register machine with program prog(e). Prove that {e N | e = one} is register machine undecidable (where one is the function mentioned in part (b)). State carefully any standard results that you use in your proof. [4 marks] 4 CST.2014.6.5 4 Computation Theory (a) Give the recursion equations for the function n (f, g) N n+1 N defined by primitive recursion from functions f N n N and g N? n+2 N. [2 marks] (b) Define the class PRIM of primitive recursive functions, giving exact definitions for all the functions and operations you use. [5 marks] (c) Show that the addition function add(x, y) = x + y is in PRIM.

(a) Define what it means for a set of numbers S N to be register machine decidable. Why are there only countably many such sets? Deduce the existence of a set of numbers that is not register machine decidable. (Any standard results that you use should be clearly stated.) [4 marks] (b) A set of numbers S N is said to be computably enumerable if either it is empty or equal to {f(x) | x N} for some total function f : N N that is register machine computable. (i) Show that if S is register machine decidable, then it is computably enumerable. [Hint: consider separately the cases when S is, or is not empty.] [4 marks] (ii) Show that if both S and its complement {x N | x / S} are computably enumerable, then S is register machine decidable. [Hint: consider a register machine that interleaves the enumeration of S and its complement.]

A hardware engineer stores a FIFO queue of bits in an int on a platform with 32-bit ints and 8-bit chars using the following C++ class: class BitQueue { int valid_bits; //the number of v?alid bits held in queue int queue; //least significant bit is most recent bit added public: BitQueue(): valid_bits(0),queue(0) {} void push(int val, int bsize); int pop(int bsize); int size(); };ODE formula. What is the order of each of the methods (1) and (2)? [2 marks] (b) Giving answers to 2 significant decimal digits of accuracy, compute the solution of the ODE for xn = 0, 0.1, 0.2, . . . 1.0 for each method. Tabulate your answers. The exact solutions to 2 significant digits are: 1.0, 0.61, 0.37, 0.22, 0.14, 0.082, 0.050, 0.030, 0.018, 0.011, 0.0067 Assume the exact value of y(0.1) for method (2). [7 marks] (c) Which method is more accurate initially and why? Peruse the paper in the beneath referenced connection and help in finishing the accompanying things:

Issue proclamation: Defines what is the issue that the creators are attempting to address. Foundation: Talks about the subject foundation or potentially related data about the issue or the other existing arrangements. Arrangement Approach: Shows the framework block graph for your current circumstance. Fundamentally saying how the creators tackle the issue that was referenced in the "Issue Statement" segment. Framework Implementation: Demonstrates the creators center work including however not restricted to setting applied, programming utilized, and so on. Result or potentially test run: Shows the screen captures of the outcome structure the paper. Perceptions/Discussions: Gives the finish of this examination/paper. Reference is set in the underneath connect:

https://drive.google.com/record/d/1z-cPUVBug4xcEAy-wKvVIHN2qojUocI0/view?usp=sharing

References:

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[2] F. Xia, W. Wang, T. M. Bekele, and H. Liu, ''Big academic information: An overview,'' IEEE Trans. Enormous Data, vol. 3, no. 1, pp. 18-35, Mar. 2017. [3] C. Caragea et al., ''Automatic distinguishing proof of examination articles from crept archives,'' in Proc. Studio Web-Scale Classification, Classifying Big Data Web, New York, NY, USA, 2014, pp. 1-6.

[4] S. Lehmann, A. D. Jackson, and B. E. Lautrup, ''Measures for measures,'' Nature, vol. 444, no. 7122, pp. 1003-1004, 2006.