large sampling multi-volume encyclopedia like the Encyclopaedia Britannica. Describe in detail the ways in which you would organise and index the encyclopedia text, and the facilities you would offer the system user. [12 marks] Justify your choices. [4 marks] Comment on the issues that would arise if you wanted to evaluate system performance. [4 marks] 6 Security You have been hired by a company which is bidding to take over the National Lottery when Camelot's franchise expires, and your responsibility is the security architecture. State the security policy you would recommend and outline the mechanisms you would implement to enforce it.

) (i) Define the notion of a register machine and the computations that it carries out. [5 marks] (ii) Explain, in general terms, what is meant by a universal register machine. (You should make clear what scheme for coding programs as numbers you are using, but you are not required to describe a universal register machine program in detail.) [5 marks] (b) (i) Explain what it means for a partial function f from N to N to be computable by a register machine. [2 marks] (ii) Let n > 1 be a fixed natural number. Show that the partial function from N to N fn(x) = n nx if x > 0 undefined if x = 0 is computable. [3 marks] (iii) Explain why there are only countably many computable functions from N to N. Deduce that there exists a partial function from N to N that is not computable. (Any standard results you use about countable and uncountable sets should be clearly stated, but need not be proved.) [3 marks] (iv) If a partial function f from N to N is computable, how many different register machine programs are there that compute f? [2 marks] 8 Artificial Intelligence I We have a basic search problem, consisting of a set S of states, a start state s0, a goal test G(s) that returns True if s S is a goal and False otherwise, and a function exp(s) that returns the set of states obtained by expanding state s. (a) Describe in detail the Graph Search algorithm for solving a problem of this type. How does it differ from the related Tree Search algorithm? [8 marks] (b) Give a detailed description of the Recursive Best First search algorithm, and explain why it might be used in preference to the A? algorithm. [12 marks] 7 (TURN OVER) CST.2007.3.8 9 Introduction to Security (a) You have received a shipment of hardware random-number generators, each of which can output one 128-bit random number every 10 milliseconds. You suspect that one of these modules has been tampered with and that it actually produces only 30-bit random numbers internally, which are then converted via a pseudo-random function into the 128-bit values that it outputs. (i) How does this form of tampering reduce the security of a system that uses a generated 128-bit random number as the secret key of a block cipher used to generate message authentication codes? [2 marks] (ii) Suggest a test that has a more than 0.5 success probability of identifying within half an hour that a module has been tampered with in this way. [6 marks] (b) Explain briefly (i) the encryption and decryption steps of Cipher Feedback Mode; [3 marks] (ii) why some operating systems ask the user to press a special key combination (e.g., Alt-Ctrl-Del) before each password login; [3 marks] (iii) how a secure hash function can be used to implement a one-time signature scheme; [3 marks] (iv) what happens if the same private key of the scheme from (iii) is used multiple times, to sign different messages.

Write Java program to read a full names (first and last together) from a text file and print the name in the' last, first' java program to read a last name. Print the number of characters in the name and also the number of vowels in the name.

Explain the mechanisms and computational significance of nerve impulse generation and transmission. Discuss each of the following aspects: (a) The equivalent electrical circuit for a nerve cell membrane. (b) How different ion species flow across the membrane, in terms of currents, capacitance, conductances, and voltage-dependence. (Your answer can be qualitative.) (c) The role of positive feedback and voltage-dependent conductances. (d) The respect in which a nerve impulse is a mathematical catastrophe. (e) The approximate time-scale of events, and the speed of nerve impulse propagation. (f ) What happens when a propagating nerve impulse reaches an axonal branch. (g) What would happen if two impulses approached each other from opposite directions along a single nerve fibre and collided. (h) How linear operations like integration in space and time can be combined in dendritic trees with logical or boolean operations such as AND, OR, NOT, and veto. (i) Whether "processing" can be distinguished from "communications", as it is for artificial computing devices. (j) The respects in which stochasticity in nerve impulse time-series may offer computational opportunities that are absent in synchronous deterministic logic. [2 marks each] 5 [TURN OVER CST.99.7.6 8 Natural Language Processing Write about two of the following. Describe how each technique can be used in the solution of a natural language processing (sub)task and the problems which remain. (a) Active chart parsing (b) Part-of-speech disambiguation using finite-state machines (c) Probabilistic context-free grammar

Give a parametric definition of a torus centred at the origin and aligned with the coordinate axes. [4 marks] Outline how you would find the first intersection point, if any, of a ray with the torus from the previous part. [You may assume that you are provided with functions to find the roots of linear, quadratic, cubic and quartic equations.] [4 marks] Show how to construct a circle using non-uniform rational B-splines (NURBS). [8 marks] Show how the circle definition from the previous part can be used to define a NURBS torus. [You need explain only the general principle and the location of the torus's control points.] [4 marks] 7 [TURN OVER CST.99.7.8 12 Types Contrast the advantages and disadvantages of explicit and implicit typing. [4 marks] Consider an ML-style language with types and type schemes ::= | bool || list ::= A ( ) Give the typing rules for variables, function abstraction, function application, and let-binding. Make the form of the typing judgement clear. [5 marks] Give terms M1 and M2 such that N1 is typable (in the empty context) and N2 is not, where N1 def = letvalf = M1 inM2 end N2 def = (fn f M2) M1 Give all uses of required in a typing derivation for N1; prove that there does not exist a typing derivation for N2. [7 marks] What is a principal type scheme? Give the principal type scheme for N1, or explain informally why it does not have one.