)))(Now express your DFT sequence F[k] using a series with only N/2 terms, by capturing the second half of the series within the first half, and show that fewer complex multiplications are required. [4 marks] (iii) Now show that separating F[k] into two new sequences of half-length, each of which computes only N/2 coefficients F[k], leads to a very efficient recursive form. How many times can this halving process be repeated? Ultimately how many complex multiplications are therefore required for this Fast Fourier Transform (FFT)? For 'big data' applications requiring a DFT on a billion data values, what speed-up factor can be expected by using an FFT instead of explicitly computing a DFT? [4 marks] (c) Piecewise continuous and absolutely integrable functions f(x), g(x) : R ? C have Fourier transforms F(?) and G(?), respectively. Let h(x) = (f ? g)(x) be the convolution of f(x) and g(x): h(x) = Z ? ?? f(x ? y)g(y)dy Prove that H(?), the Fourier transform of h(x), is simply the product: H(?) = 2?F(?) G(?) [4 marks] 7 (TURN O CST1.2017.6.8 8 Mathematical Methods for Computer Science (a) (i) State the central limit theorem. [2 marks] (ii) Consider a binomially distributed random variable T with parameters Bin(n,p) where n is a positive integer and 0 d) where d ? (0, n) and where n is sufficiently large.?

Suggest how you would represent Lambda-expressions in a form suitable for a simple Lambda-evaluator in which the environment is represented as a linked list of name- value pairs. [5 marks] Outline the design of the evaluator, paying particular attention to the treatment of bound variables, abstractions and applications. [5 marks] Augment your evaluator to cope with sufficient expression operators, including a built-in version of the Y operator so that when the evaluator is given the abstract syntax tree for Y (?f.?n. n=0 -> 1, n*f(n-1)) 5 it will yield 120. [10 marks] 7 Artificial Intelligence I Compare and contrast heuristic search and exhaustive search. [6 marks] Which compromises are accepted by the heuristic approach? [8 marks] Illustrate your answer with examples of heuristics. [6 marks] 8 Databases What are the primitives in terms of which a network data model is presented? [4 marks] Explain how such a data model is specified in the CODASYL Schema Data Definition Language. [6 marks] How does an application programmer in COBOL gain access to a CODASYL database? [3 marks] Describe the COBOL programmer's model of the database, illustrating your answer with suitable data manipulation commands. [7 marks] 3 [TURN OVER CST.94.12.4 9 Specification and Verification of Hardware Briefly discuss each of the following topics: (a) the representation of schematic diagrams in predicate calculus [5 marks] (b) the use of primitive recursion in hardware specification [5 marks] (c) modelling combinational and sequential circuits [5 marks] (d) temporal abstraction [5 marks] 10 Complexity What is a? Hamiltonian Circuit? What is the Boolean Satisfiability Problem "3-SAT"? words each, sketch (a) how an efficient solution to 3-SAT would allow you to construct an efficient solution to the Hamiltonian Circuit problem [6 marks] (b) how an efficient solution to the Hamiltonian Circuit problem would allow you to solve 3-SAT [6 markst by "efficient" in this context

Suppose that we have defined a view V = Q(R1, R2, . . . , Rn), where the Ri indicate the base tables used in query Q. The designers of a new database system want to allow users to update directly such a view. That is, if we have an update of the form U = insert(V, t) or U = delete(V, p), then the database system must automatically generate a transaction TU over the tables Ri such that for any database instance DB this diagram commutes: DB TU ?? DB0 ? Q ? Q V U ?? V 0 In other words, applying the update U directly to a view (as if it were a base table) produces the same result as applying TU to the database and then evaluating the view query. A major problem with this approach is that there may be multiple distinct solutions for TU . We explore this now. (a) Explain the difference between a database query and a database view. [2 marks] (b) Let V = ?X(R) be a view for some base table R and some subset X of R's attributes Y . How could this be translated into the desired transaction TU ? Discuss any problems with ambiguity that may arise. [5 marks] (c) Let V = ?q(R) be a view for some base table R and predicate q. How could this be translated into the desired transaction TU ? Discuss any problems with ambiguity that may arise. [5 marks] (d) In the design of a database schema it was discovered that a relation R violated Boyce-Codd normal form, and so it was replaced by two base tables R1 and R2 resulting from the standard decomposition process. Suppose users attempt to reconstruct the original relation using the view V = R1 ? R2. Discuss the problems that might arise now in the construction of transaction TU for updates to V . [8 marks] 6 CST.2015.4.7 7 Economics, Law and Ethics (a) Describe three different philosophies of ethics. [12 marks] (b) Which of these philosophies might be more, or less, attractive to a successful businessman who made his money from coal or steel? Justify your answer. [4 marks] (c) Might a tech billionaire whose fortune is founded on network effects take a different view? Justify your answer. [4 marks] 8 Security I (a) Compare and contrast the security definitions of a pseudo-random generator and a pseudo-random function. [4 marks] (b) When a Windows NTFS access control entry (ACE) is inherited by a subdirectory, under which circumstances is the "inherit only" flag set or cleared, and why? [4 marks] (c) What is existential unforgeability of a message authentication code? [4 marks] (d) Which problem with CBC-MAC is fixed by ECBC-MAC, and how? [4 marks] (e) A C program running on a 32-bit processor contains the following function: void f(int *a, int l) { int *b, i; b = (int *) malloc(l * sizeof(int)); if (b == NULL) return; for (i = 0; i

2. Assignment Report Instructions: Description Number of Pages 1 Cover page (Course name and number, professor name, name of the group members, date) 1 page 2 Introduction / Executive summary about the market research 1 page 3 The customer concern/Issue - the need for the new/enhanced product 1 page 4 Summary of VOC including the method(s) used to gather information about the customer 1 page requirements with references 5 The Business Plan and Marketing Strategy for the new/enhanced product. The business plan shall 5 pages include the components as illustrated in the figure in the next slide. 6 References with proper citation (Check citation resources at the bottom of the home page of your 1 Page eConestoga course shell. 7 Report format: Word/Pdf file, Times New Roman font with 12 pts size and 1.5 line spacing 10 pages 8 Upload the assignment report to the drop box in the course shell - eConestoga by the due date (Only one member from the group shall submit the assignment report) 3. Some examples of new/enhanced products could be to enhance the customer experience of waste segregation and management (different than the product we discussed in week 4), snow removal, digital 3 devices' screen cleaning, ..etc