infom Hence find the posterior distribution of (z, ). Your answer…
Question Answered step-by-step infom Hence find the posterior distribution of (z, ). Your answer… infomHence find the posterior distribution of (z, ?). Your answer may be left as anun-normalised density function. [5 marks](d) Find the posterior distribution of z. [5 marks]My colleague has more grant money and she can employ 3 workers to rate each image.On a test set of 30 images, she found that they all agreed on 15 images, worker 1 wasthe odd one out on 8 of the images, worker 2 was the odd one out on 4, and worker 3was the odd one out on 3.(e) Let ?i be the probability that worker i labels an image incorrectly. Find theposterior distribution of (?1, ?2, ?3)Concurrent and Distributed Systems Database concurrency control enables multiple transactions to proceed simultaneously against a shared database. (a) Give an example each of conflicting and non-conflicting operations on objects in a database. [2 marks] (b) Explain how timestamp ordering (TSO) works, and how it responds to conflicts between transactions. [4 marks] (c) Explain cascading aborts, and use an example to show how they can occur with TSO. [4 marks] (d) Why is TSO not subject to deadlock? [2 marks] (e) Explain why TSO distributes well, compared with two-phase locking. [4 marks] (f ) Construct a workload that performs badly under TSO, and explain why it does so. What could you do to improve its performance? e { void push(Object val); Object pop(); }; (i) Write pseudocode for a semaphore-based implementation of Queue. Your implementation should allow concurrent push and pop when it is safe to do so, but not when it is unsafe. The queued data should be stored in an array of fixed length n. [6 marks] (ii) Explain the specific circumstances under which concurrent push and pop is unsafe. Explain how your solution in part (i) addresses these. [2 + 2 marks] (b) You decide to use this data structure to manage a service, where people around the world push jobs of work to be done, and others pop jobs and do them. (This is a description of Amazon’s Mechanical Turk.) This could be implemented as a centralised service, offered through ObjectOriented Middleware. (i) How can the Object-Oriented Middleware maximise the utilisation of this service? [2 marks] (ii) Object-Oriented Middleware makes the calls to push and pop look local. Name two things that this hides from the programmer using the service and say why each is a problem.answer every questionLet E, F be events over a finite alphabet S. Define the events E + F, EF andE*. [3 marks]Show that:(a) E* = 1 + EE*(b) E(F E)* = (EF)*E Describe the state-variable representation for planning by discussing thefollowing, giving specific examples of each concept:(i) Rigid relations and state variables. [2 marks](ii) Actions. [2 marks](iii) The representation of state. [2 marks](iv) Goals and solutions. [2 marks](b) Your boss has suggested using heuristic search to solve a planning problemexpressed in the state-variable representation. Explain how this might beachieved. You do not need to suggest a specific heuristic at this stage.[3 marks](c) Comment on whether or not heuristic search is a good approach to solvingplanning problems in the state-variable representation, compared with thealternative of using a constraint satisfaction solver. [5 marks](d) Suggest an admissible heuristic that could be used when applying A?search tosolving a planning problem in the state-variable representation. Show that it isadmissible. [4 marks]3 (TURN OVER)CST1.2019.6.43 Complexity TheoryA Boolean formula ? is said to be satisfiable if there is an assignment ? : V ?{true, false} of values to the variables of ? that makes it true.A quantified Boolean formula ? is an expression that is (i) either a Boolean formula;or (ii) ?X? where ? is a quantified Boolean formula and X is variable; or (iii) ?X?where ? is a quantified Boolean formula and X is variable.We say that a quantified Boolean formula ? is satisfied by an assignment ? : V ?{true, false} if either ? is a Boolean formula that is made true by ?; or ? is ?X? and either ?[X/true] or ?[X/false] make ? true; or ? is ?X? and both ?[X/true] and ?[X/false] make ? true.Here, ?[X/v] denotes the assignment that is the same as ? for all variables apartfrom X, and it maps X to the truth value v.We write QBF for the decision problem of determining whether a given quantifiedBoolean formula is satisfiable. In answering the questions below, you may assumethe NP-completeness of any standard problem, as long as you state your assumptionsclearly.(a) Show that QBF is NP-hard. [4 marks](b) Show that QBF is co-NP-hard. [6 marks](c) Show that QBF is in PSpace. [6 marks](d) Is QBF NP-complete? Why or why not? [4 marks]4CST1.2019.6.54 Complexity TheoryA Boolean formula ? is in conjunctive normal form (CNF) if it is the conjunctionof clauses, each of which is the disjunction of literals. It is said to be in k-CNF (fork ? N) if each clause has exactly k literals in it.An assignment ? : V ? {true, false} of truth values to the variables is a satisfyingassignment for a CNF formula ? if it makes at least one literal in each clause of ?true. It is said to be a not-all-equals assignment for ? if it makes at least one literalin each clause of ? true and at least one literal in each clause of ? false.Let CNF-SAT denote the problem of determining, given a formula in CNF, whetherit has a satisfying assignment.Let k-SAT denote the problem of determining, given a formula in k-CNF, whether ithas a satisfying assignment.Let k-NAE denote the problem of determining, given a formula in k-CNF, whetherit has a not-all-equals assignment.(a) Explain why CNF-SAT is NP-complete. Your explanation should include a fulldefinition of NP-completeness and a brief sketch of the proof of the Cook-Levintheorem. [5 marks](b) Show that 3-SAT is NP-complete by means of a suitable reduction. [3 marks](c) Give a polynomial-time reduction from 3-SAT to 4-NAE. What can you concludeabout the complexity of the latter problem?(Hint: consider introducing one new variable and adding it to every clause.)[8 marks](d) Show that the problem 3-NAE is NP-complete.(Hint: consider a reduction from 4-NAE) What is the maximum number of terms there can be in a minimal sum of productsform of a function of n boolean variables? [2 marks]Consider a two-bit multiplier with inputs x1, x0, y1, y0 and outputs z3, z2, z1, z0 suchthatZ = Y × Xwhere Z, Y, X are the positive integers represented by z3z2z1z0, y1y0 and x1x0using the obvious representation.Find a minimal sum of products expression for each of z3, z2, z1 and z0. [10 marks]Comment on the complexity of building an eight-bit multiplier using a minimalsum of products form. [3 marks]Describe another way of building an eight-bit multiplier. Describe the characteristic features of a VLIW (Very Long Instruction Word)processor architecture. [3 marks]VLIW processors aim to achieve high execution throughput using a differentstrategy from that of out-of-order dynamic execution RISC implementations.Compare and contrast these different approaches, pointing out the advantages anddisadvantages of each strategy in achieving this goal.You may wish to consider the following issues: instruction issue logic cache sizes compiler code generation execution unit utilisation[9 marks]Why have VLIW architectures traditionally been used only for special-purposeapplications such as Digital Signal Processors?What techniques have been developed to make VLIW-like architectures moresuitable for general-purpose use? [5 marks]3 [TURN OVERCST.2000.7.44 Information RetrievalYou work for a large company where there are many meetings, both of internal staffand between staff and external clients. Meetings are recorded in formal minutes.The company’s files of minutes are large, and the material has to be kept for manyyears since it may be necessary to check back on decisions taken early in largeprojects.You are asked to design a retrieval system so that company staff can locate minuteson a particular topic. Because of the legal implications that past discussions anddecisions may have, the company is particularly concerned that the new retrievalsystem will be reliable and effective.Outline the design of your system, indicating the particular features it will have thatare intended to meet the company’s requirements (you can assume that minutesare always clearly dated and have explicit lists of participants). [10 marks]The company is willing to allow the installation of a pilot system so your approachcan be evaluated under realistic conditions.Describe, in detail, your design for the evaluation: what data, operationalconditions and aspects of your system would you consider, and why? Whatperformance measures would you apply, and why? [10 marks]5 Security”Robert Morris Senior was responsible for Unix security, Robert Morris Junior forthe Internet worm. The father did much more damage to Internet security thanthe son” (Whitfield Diffie). Discuss. [20 marks]4CST.2000.7.56 Neural ComputingExplain the key ideas of a Hopfield artificial neural network for content-addressable,associative memory. In explaining how memories are stored and retrieved, be sureto define the notions of: configuration space connectivity matrix stable attractor basin of attraction network capacity, and its dependence on the number of “neurones”[10 marks]Marshall as many lines of evidence as you can to support the view that in humanvision “what you see is your own ‘graphics’, rather than the retinal image asfaithfully recorded by photoreceptors in the eye”. Explain the significance of thisobservation for vision theory and for machine vision. [8 marks]Suppose you were trying to design a machine vision system based as closely aspossible upon human vision. Would you aim to design in the visual illusions thatnearly all people “see” as well? (These include the distortions of geometrical form,angle and relative length illusions, etc.) If such properties emerged as unintendedconsequences of your vision design, would you consider them to be features, orbugs? [2 marks]5 [TURN OVERCST.2000.7.67 Natural Language ProcessingThe following context-free grammar and lexicon generates the examples below itwith multiple derivations and therefore multiple associated interpretations.(a) S ? NP VP(b) NP ? Det N(c) NP ? NP PP(d) N ? N N(e) VP ? V NP(f ) VP ? V NP PP(g) VP ? VP PP(h) PP ? P NPN ? car | park | tree | boy | toy | morning | . . .V ? hit | . . .P ? in | with | . . .Det ? a | the | . . .a car hit the tree in the parkthe boy hit the toy car park with a toy car in the morningDescribe how a probabilistic version of the context-free grammar (PCFG) can becreated, defining the constraints which must hold for the resulting PCFG to beinterpretable as a stochastic language model. [8 marks]How accurate would the resulting PCFG be at assigning the semanticallyappropriate derivations the highest probability for the examples and otherstructurally similar sentences? [6 marks]Define an improved probabilistic model for discriminating alternative derivations.What problems would arise in the implementation of this model? [6 marks]6CST.2000.7.78 Computer System ModellingWhat is meant by the term memoryless as used in describing a Markov chain?[3 marks]What limitation does this place on using Markov chains to model real systems?[3 marks]”As systems become saturated their response time becomes unpredictable.”Why is this? Illustrate your answer using an M/M/1 queueing system. [10 marks]Show, by drawing the state transition diagram of a Markov chain, how arrivalprocesses with inter-arrival times that are not exponentially distributed can bemodelled.The following is the start of a Java program which is intended to print out all primenumbers below 600.public class Primes{ private static final int SIZE=600, SQRTSIZE=25;public static void main(String[] args){ boolean[] primes = new boolean[SIZE];for (int i=2; i
