answer the question clearly

(a) Write down an expression for the distribution Pr(n|) where n {1, . . . , 9}. [2 marks

You are preparing to participate in a password-cracking competition. During the competition, you will be given the 128-bit hash-function output MD5(p). You have to find p, an 8-character password, each character having been chosen uniformly at random from a known alphabet of 64 ASCII characters. In the weeks preparing for the competition, you have access to a small cluster of GPU graphics cards that can evaluate MD5 109 times per second. During the competition, you have only access to a laptop computer that can evaluate MD5 106 times per second. Without any pre-computation, how long would it take to evaluate MD5 for all possible passwords p in a brute-force attack (i) on the laptop? [2 marks] (ii) on the GPU cluster? [2 marks] You decide to use the GPU cluster to pre-compute a rainbow table for this challenge. (iv) Your laptop has enough RAM for storing the rainbow table as a hash table

This question deals with stochastic processes {N(t), t 0} where N(t) represents the number of events in the time interval [0, t]. (a) (i) Define a Poisson process {N(t), t 0} of rate > 0. [2 marks] (ii) Show that N(t) Pois(t) for each fixed t > 0. You may use the result that limn(1 x/n) n = e x without proof. [4 marks] (iii) Let X1 be the time of the first event of the Poisson process N(t). Show that X1 Exp(). (iv) Now given that N(t) = 1 derive the distribution of the time of the single event in [0, t]. [4 marks] (b) Suppose that events of a Poisson process of rate are independently selected at random with probability p > 0. Show that the process of selected events is also a Poisson process and establish its rate. [2 marks]

a) Why does pipelining introduce data hazards? [4 marks] (b) What mechanism may be used to remove some dards? [4 marks] (c) Why is it not possible to remove all data hazards? [4 marks] (d) What hardware is required to prevent data hazards from infringing the programmer's model of instruction execution? [4 marks] (e) What is the difference between a data hazard and a control hazard? [4 marks] 5 [TURN OVER CST.2001.3.6 7 Operating System Functions (a) What are the key issues with scheduling for shared-memory multiprocessors? [3 marks] (b) Processor affinity, take scheduling and gang scheduling are three techniques used within multiprocessor operating systems. (i) Briefly describe the operation of each. [6 marks] (ii) Which problem does the processor affinity technique seek to overcome? [2 marks] (iii) What problem does the processor affinity technique suffer from, and how could this problem be overcome? [2 marks] (iv) In which circumstances is a gang scheduling approach most appropriate? [2 marks] (c) What additional issues does the virtual memory management system have to address when dealing with shared-memory multiprocessor systems?

Five housemates run a "status" server on their home network. The server stores the current status of each housemate as a string of text. For example, housemate Eva might set her status to "Gone to the exam hall." Messages are passed between clients and the server as text strings sent over TCP. The new line character is used exclusively as the last character in every message. On connection with the server, a client can either (i) query the status of a user by sending the user's name to the server as a string (and the server responds with the current status message), or (ii) set the status of a user by sending the user's name followed by a colon and the new status message. For example, "Eva:Gone to the exam hall." sets the status message for Eva. (a) Implement a status server in Java. The server should run indefinitely, responding to client requests. Once a client request has been fulfilled, the server should close the connectiona) Why does pipelining introduce data hazards? [4 marks] (b) What mechanism may be used to remove some dards? [4 marks] (c) Why is it not possible to remove all data hazards? [4 marks] (d) What hardware is required to prevent data hazards from infringing the programmer's model of instruction execution? [4 marks] (e) What is the difference between a data hazard and a control hazard? [4 marks] 5 [TURN OVER CST.2001.3.6 7 Operating System Functions (a) What are the key issues with scheduling for shared-memory multiprocessors? [3 marks] (b) Processor affinity, take scheduling and gang scheduling are three techniques used within multiprocessor operating systems. (i) Briefly describe the operation of each. [6 marks] (ii) Which problem does the processor affinity technique seek to overcome? [2 marks] (iii) What problem does the processor affinity technique suffer from, and how could this problem be overcome? [2 marks] (iv) In which circumstances is a gang scheduling approach most appropriate? [2 marks] (c) What additional issues does the virtual memory management system have to address when dealing with shared-memory multiprocessor systems?

Five housemates run a "status" server on their home network. The server stores the current status of each housemate as a string of text. For example, housemate Eva might set her status to "Gone to the exam hall." Messages are passed between clients and the server as text strings sent over TCP. The new line character is used exclusively as the last character in every message. On connection with the server, a client can either (i) query the status of a user by sending the user's name to the server as a string (and the server responds with the current status message), or (ii) set the status of a user by sending the user's name followed by a colon and the new status message. For example, "Eva:Gone to the exam hall." sets the status message for Eva. (a) Implement a status server in Java. The server should run indefinitely, responding to client requests. Once a client request has been fulfilled, the server should close the connection, re-write the grammar to reflect this. [4 marks] (c) List the terminal symbols and non-terminal symbols, and count the production rules both in the original grammar and in the grammar in your answer to part (b). Indicate the start symbol in both grammars. [2 marks](d) Define a type or types (in C, Java, or ML) suitable for holding an abstract syntax tree resulting from your answer to part (b). [2 marks] (e) Give a brief and elementary explanation of the principles of how the grammar resulting from part (b) might be used to create a syntax analyser taking a token stream as input (via calls to function lex()) and giving as output an abstract syntax tree corresponding to part (d). Mention both hand-written and automatically-generated syntax analysers. (i) Provide its channel matrix. [3 marks] (ii) Give the average probability of correct reception, meaning the probability that the same symbol is emitted as was injected into the channel, averaged over all the cases. [3 marks] (b) Show that convolution of any continuous signal with a Dirac delta function reproduces the signal. [4 marks] (c) A frequency-shifting modulation of signals into different channels of a shared medium multiplies the baseband signal f(t) by a complex exponential carrier wave e ict of some (channel-specific) frequency c to produce a passband f(t) e ict (see figure below). Upon reception of such a passband, what process of demodulation would recover the original baseband? baseband carrier signal AM passband FM passband [5 marks] (d) Explain the "information diagram" of Gabor, and why the Uncertainty Principle gives it a quantal structure with an irreducible representation of the data. [5 marks] 12 CST.2016.7.13 11 Natural Language Processing The distributional hypothesis states that the meaning of a word can be defined by its use and, therefore, it can be represented as a distribution of contexts in which the word occurs in a large text corpus. (a) Describe four different types of context that can be used for this purpose. [4 marks] (b) The contexts can be weighted using Pointwise Mutual Information (PMI). Explain, giving formulae, how PMI is calculated and how individual probabilities are estimated from a text corpus. [5 marks] (c) Some words occur very rarely in the corpus. How does this affect their PMI scores as contexts? [4 marks] (d) The goal of distributional word clustering is to obtain clusters of words with similar or related meanings. The following clusters have been produced in two different noun clustering experiments: Experiment 1: carriage bike vehicle train truck lorry coach taxi official officer inspector journalist detective constable policeman reporter sister daughter parent relative lover cousin friend wife mother husband brother father Experiment 2: car engine petrol road driver wheel trip steering seat highway sign speed concert singer stage light music show audience performance ticket experiment research scientist paper result publication laboratory finding (i) How are the clusters produced in the two experiments different with respect to the similarity they capture? What lexico-semantic relations do the clusters exhibit? [3 marks] (ii) The same clustering algorithm, K-means, was used in both experiments. A multinational company has started a project to launch its Branches in different countries and the company is going to start its Business and initially its network wll be developed for six countries i.e. Pakistan,Saudi Arabia, China, Austria,Japan, and Brunei Darussalam. These countries may be named as a, b, c d, e,f respectively and Company has planned to establish the Communication Channels for its proper smooth business .The costis given in the following table to establish the communication link .Which Communication Channels will be developed to ensure that all countries are connected so thatthe total cost of the Mega Project is minimized? A multinational company has started a project to launch its Branches in different countries and the company is going to start its Business and initially its network wll be developed for six countries i.e. Pakistan,Saudi Arabia, China, Austria,Japan, and Brunei Darussalam. These countries may be named as a, b, c d, e,f respectively and Company has planned to establish the Communication Channels for its proper smooth business .The costis given in the following table to establish the communication link .Which Communication Channels will be developed to ensure that all countries are connected so thatthe total cost of the Mega Project is minimized?ders the set of all points P in space where the forces of the functions sum to a threshold: the 3D isosurface such that PFi(P) = 0.5. (a) Using pseudocode, give a force function Sphere(P) which will render a unit sphere centred on (0, 0, 0). [Figure 1] [2 marks] (b) Using pseudocode, give a force function Cube(P) which will render an axisaligned cube of edge length 2 centred on (1, 1, 1). [Figure 2] [4 marks] (c) You now pass both Sphere(P) and Cube(P) to your implicit surface renderer. Depending on your choice of force functions, the seam between the cube and the sphere may be a sharp edge (to within the tolerance of your polygonalization) or a smooth blend which merges gradually from one form into the other. Which will it be, and (briefly) why? [Figures 3 and 4] [2 marks] (d) Provide alternate formulations of Sphere(P) and/or Cube(P) such that if you answered 'smooth' to Part (c) then your answer would now be 'sharp', or vice-versa. [4 marks] A spatial distortion function S : R 3 R 3 transforms one 3D point to another. If the points passed into the force function are modified by a spatial distortion functionthat is, if we render F(S(P))then the rendered isosurface will have a different shape. For example, if we define S(P) as function Point S(P) { return new Point(P.x * 2, P.y / 2, P.z * 2); } then rendering the implicit surface of Sphere(S(P)) will yield a tall, narrow ellipsoid along the Y axis. [Figure 5] (e) Give a spatial distortion function S(P) such that rendering the isosurface of Cube(S(P)) would render the cube centred at the origin and rotated 45 degrees around the X axis. [Figure 6] Hint: a standard rotation matrix is cos(t) sin(t) sin(t) cos(t) . [3 ma