Describe the AC-3 algorithm for enforcing arc consistency. If you need some support data, here it is: Support Details for the question - [5 marks] (e) Prove that the time complexity of the AC-73 algorithm is O(n 2d 31 ) where d is the size of the largest domain. What can we conclude about the functional dependency Z W? Explain your answer. [4 marks] (c) In the process of using functional dependencies to normalise a schema, what is meant by a lossless join decomposition and how is such a decomposition guaranteed? [4 marks] (d) In schema normalisation, is Boyce-Codd Normal Form (BCNF) always to be preferred over 3rd Normal Form (3NF)? Explain your answer. [4 marks] Explain the term hidden bit. What are the values of the hidden bit for normalised and denormal numbers? How is the exponent stored and why? How are the exponent, significand and sign bit arranged in memory? [4 marks] (c) Let x denote the floating-point representation of a number x. Define the terms absolute error (x) and relative error (x) in representing x. How are x and x related? When two fluids are mixed the resultant temperature is the sum of their initial temperatures weighted by their proportions. (a) Give a suitable state vector for a simple, finite-difference, time domain simulation of the drink system. [3 marks] (b) List the initial values and any other parameters that are needed for the simulation. (iii) Can the grouping operator be used to define the projection operator? Justify your answer. [2 marks] 8 CST.2004.13.9 9 Numerical Analysis II List the terminal images and non-terminal images, and count the creation rules both in the first syntax and in the sentence structure in your response to part (b). Demonstrate the beginning image in the two sentence structures. [2 marks] (d) Define a sort or types (in C, Java, or ML) Objects 2 : Electronic health records (EHRs) in a nationwide service. Policy: The owner (patient) may read from its own EHR. A qualified and employed doctor may read and write the EHR of a patient registered with him/her. (iv) Object: The solution to online coursework. Policy: The coursework setter has read and access. A candidate has no access until after the marks have been published. [8 marks each] 4 CST.2004.13.5 5 Computer Graphics and Image Processing (a) Explain why display devices appear to be able to reproduce (almost) all the colours of the spectrum using only red, green and blue light Explain the terms Riemann sum and mesh norm. [4 marks] (b) Consider the quadrature rule If [a, b] = [1, 1] find 4 and hence show that this is a Riemann sum. [3 marks] (c) Suppose R is a rule that integrates constants exactly over [1, 1], and that f(x) is bounded and Riemann-integrable over [a, b]. Write down a formula for the composite rule (n R)f and prove that limn (n R)f = Z b a f(x) dx [6 marks] (d) What is the formula for (n Q)f over [a, b]? [4 marks] (e) Which polynomials are integrated exactly by Qf? Which monomials are integrated exactly by the product rule (Q Q)F when applied to a function of x and y? [3 marks] 9 [TURN OVER CST.2004.13.10 10 Introduction to Functional Programming (a) Define a polymorphic datatype 'a tree to represent binary trees. [1 mark] (b) A breadth-first traversal of a tree walks over all the nodes at each level before proceeding to the next level. For example the breadth-first traversal of the tree: 6 7 visits the nodes in the order 6, 7. Define a function breadth: 'a tree -> 'a list such that breadth(t) returns the nodes of tree t in breadth-first order. [10 marks] (c) Define a polymorphic datatype 'a seq to represent lazy lists. [1 mark] (d) Define a polymorphic datatype 'a ltree to represent lazy binary trees. [3 marks] LibApp Module the LibApp module as follows Add the following attributes to the LibApp Module. File name Add an array of 2156 characters to hold the publication data file name. Publication Pointers Array and add an array of Publication pointers to the size of SDDS_LIBRARY_CAPACITY. This array will be populated with all the records of the publication data file when the LibApp is instantiated. We will call Publication Pointers Array "PPA" for short, from now on. You need specify only the classes you would define. Most of the algorithmic details may be omitted. [6 marks] (c) Discuss to what extent Simula has been made redundant by the development of modern object-oriented languages such as Java. DatabasesYou are planning and are going to send off a cell phone application which will look for to comprehend the profound state of the client, utilizing various information sources, for example, movement detecting, look acknowledgment, voice pressure estimation and the investigation of entered text. Its proclaimed intention is to empower administrations to communicate more empathically with clients. (a) Explain how to describe the structure of a collection of data using entities, attributes and relationships. [6 marks]