2 CST.2004.3.3 3 Data Structures and Algorithms Compiler Construction Programming answers should be written in some notation approximating SML or OCaml. (a) Describe what is meant by tail recursion. [4 marks] What is the difference between fully associative, set associative and direct mapped lookup? [6 marks] (c) Why are TLBs always much smaller than caches? [4 marks] (d) Which of the lookup mechanisms in part (b) is usually used for a TLB and why aren't the other mechanisms usually used? [6 marks] Compute XT X for your example. [2 marks] (c) Let A be an n n matrix with real entries. (i) We say that A is diagonalisable if there exists an invertible n n matrix P such that the matrix D = P 1AP is diagonal. Show that if A is diagonalisable and has only one eigenvalue then A is a constant multiple of the identity matrix. [3 marks] (ii) Let A be such that when acting on vectors x = [x1, x2, . . . , xn] T it gives Ax = [x1, x1 x2, x2 x3, . . . , xn1 xn] T . Write out the contents of A and find its eigenvalues and eigenvectors. Scale the eigenvectors so they have unit length (i.e. so their magnitude is equal to 1). [6 marks] 7 (TURN OVER) CST0.2019.1.8 SECTION D 7 Algorithms (a) The Post Office of Maldonia issued a new series of stamps, whose denominations in cents are a finite set D N\{0}, with 1 D. Given an arbitrary value n N\{0} in cents, the problem is to find a minimum-cardinality multiset of stamps from D whose denominations add up to exactly n. In the context of solving the problem with a bottom-up dynamic programming algorithm. . . (i) 4 CST1+CST2.2019.7.5 4 Formal Models of Language This question relates to an information source that produces symbols from an alphabet. (a) X is an information source, which produces symbols from the set {a, b, c, d, S} (i) If we assume X produces symbols with equal probability, what is the entropy of X? [1 mark] (ii) In fact, X produces symbols with non-equal probabilities. What do you know about the entropy of X compared to your previous answer? [1 mark] (iii) X produces symbols with probability distribution: p(a) = 0.4, p(b) = 0.2, p(c) = 0.2, p(d) = 0.1, p(S) = 0.1 Give an expression for the entropy of information source X. [2 marks] For what reason could this be really smart, how might you measure arrangement in this undertaking, and how about this work on your classifier in any capacity? [3 imprints

ew of the message they contain. You approach an enormous number of messages, N, which have been physically named as "Alright" and "harassing". (a) How could you at any point apply a Naive Bayes classifier to the undertaking and assess it? Depict the methodology, including how you would appraise the boundaries. [3 marks] (b) You choose to involve accuracy and review rather than precision as the assessment metric for this assignment. For what reason does this choice check out, and how are the measurements determined? [1 mark] An image generated using a polygon scan conversion algorithm, even one which makes heavy use of texture mapping, will still tend to look computer generated. 1.1.4 Examples Texture mapping is a simple way of making a polygon scan conversion (or a ray tracing) scene look better without introducing lots of polygons. The images in Figure 6 show a scene both with and without any texture maps. Obviously this scene was designed to be viewed with the texture maps turned on. This example shows that texture mapping can make simple geometry look interesting to a human observer. The images in Figure 7 were generated using polygon scan conversion. Texture map- Neil Dodgson 9 The symbol sequence produced by X represents consecutive words of a language, where S indicates whitespace. (i) Describe and provide an equation for the entropy of the language produced by the symbol sequence. [2 marks] (ii) A student observes that when a word in the language contains c it is always followed by b. Explain how this redundancy helps communication over a channel that tends to swap b with d. [2 marks] (c) Define a noisy channel and describe how it could be interpreted with respect to human language communication. [6 marks] (d) Computational Linguists have hypothesised that natural languages have evolved to be both efficient and robust to noise. Do you agree? Justify your answer by referring to information theory and giving appropriate examples. [6 marks]