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Specification and Verification II Explain how a register can be modelled either as a unit-delay, or with an explicit clock input. [4 marks] Describe the relationship between the two models. [4 marks] Design a device with input i and output o that outputs on o the sum of the inputsons of the device: (a) as an abstract sequential machine and (b) with an explicit clock input. [4 marks] State a logical relationship between the two specifications. [4 marks] 12 Communicating Automata Define the notion of weak bisimulation over a labelled transition system. [3 marks] A one-cell buffer B can be defined by B def = in.B0 , B0 def = out.B (the content of messages being ignored). in out B Define the linking operator _, in terms of basic operators, so that B _ B represents two buffer cells in sequence. in out B B [3 marks] Derive B _ B in B0 _ B from the basic transition rules, and draw the complete transition graph of B _ B. [3 marks] A lossy buffer cell L (like B except that it may lose messages) can be defined by L def = in.L0 , L 0 def = out.L+.L. Draw the complete transition graphs of both B _ L and L _ B. [4 marks] Show that B _ L 6 L _ B, by considering the state L _ B0 (accessible from L _ B) and showing that no appropriate state of B _ L can be observation equivalent to L _ B0 . [4 marks] Is L _ L B _ L true? Outline an argument to prove or disprove it. [3 marks] 6 CST.96.7.7 13 Designing Interactive Applications When a new patient applies to join a doctor's practice, personal and medical-history details must be obtained. Usually the patient (or the patient's parent in the case of young children) must fill in a form of two pages or more for inclusion in the patient's records. With the computerization of one particular doctor's practice, P1, a means is needed for entering the new patient's details. Two approaches are considered: (A) the doctor interviews the patient at the start of the initial consultation, and enters the details as they are elicited; (B) upon application, the patient or parent sits down at a computer and enters the details. Write one-sentence problem statements for each design problem. Then, drawing on your knowledge of the work of the doctor, discuss the pros and cons of the two approaches. [12 marks] Suppose two practices, P1 and P2, adopt approaches A and B respectively. Each is dissatisfied with the results. Practice P1 therefore decides to switch to approach B, installing a computer in a booth adjoining its waiting room, running the system designed for the doctor (modified only to prevent access to existing records), so that patients and parents can enter their details. Meanwhile practice P2 decides to change to approach A, loading the patient data entry program, unchanged, onto the doctor's PC so that he or she can enter the details during consultations. If you were asked to advise practices P1 and P2 on these moves, what outcomes would you predict? What analytical method would you use, in each case, to back up your predictions, and why

Name the three principal ions involved in nerve membrane current flows, and identify which two of them transit through voltage-dependent conductances. (g) What causes the refractory deadtime of about 1 msec after each nerve impulse?Consider the following story of the play Macbeth, by William Shakespeare: The characters are Macbeth, Lady-Macbeth, Duncan and Macduff. Macbeth is an evil noble. Lady-Macbeth is a greedy ambitious woman. Duncan is a king. Macduff is a loyal noble. Macbeth is weak because Macbeth married Lady-Macbeth and because Lady-Macbeth is greedy. Lady-Macbeth persuades Macbeth to want to be king. Macbeth murders Duncan using a knife because Macbeth wants to be king and because Macbeth is evil. Lady-Macbeth kills Lady-Macbeth. Macduff is angry because Macbeth murdered Duncan and because Macduff is loyal to Duncan. Macduff kills Macbeth. Construct a semantic network representing the above story. [8 marks] Show the chain of reasoning leading to Macduff killing Macbeth. [5 marks] It is possible to change the story so that Lady-Macbeth is unable to persuade Macbeth to want to be king. Augment the story to provide a reason for Lady-Macbeth's inability to persuade Macbeth to want to be king. Update the semantic network to reflect the new situation. [7 marks] 10 Numerical Analysis II Explain the terms (a) positive definite, (b) positive semi-definite for a symmetric matrix A. If a square matrix B is non-singular, which of the properties (a) or (b) most accurately describes BT B? What if B is singular? [4 marks] State Schwarz's inequality for the product AB. In what way is this modified for the product Ax, where x is a vector? What are the singular values of A, and how are they related to the l2 norm of A? In the singular value decomposition A = UWVT , what is W? [5 marks] Let x be an approximate solution of Ax = b, and write r = b Ax, e = x x. Find an expression which is an upper bound for the relative error ||e||/||x|| in terms of computable quantities. Explain how this result may be interpreted if the l2 norm is used. [8 marks] Suppose A is a 5 5 matrix and Ax = b is to be solved by singular value decomposition. If machine epsilon ' 1015 and the singular values of A are 1, 106 , 1010 , 1017 , 0 write down the generalised inverse W+ that you would use

Information is to be conveyed from A to B using automatic repeat request (ARQ), forward error correction (FEC), and lossless compression. (a) Explain the terms ARQ, FEC and lossless compression. [5 marks] (b) If we consider each of these functions to be operating at different protocol layers, what would be the most sensible ordering of the layers, and why? [5 marks] (c) Suppose: The underlying bit channel has a capacity of B, a delay and error rate 0. The compression ratio is C < 1. The FEC has rate R < 1 and given an error rate 0 provides an error rate 1 (which is detected). The ARQ protocol has a window size of W. At what rate can the information be conveyed? [Hint: Consider when retransmissions are made.] State any assumptions you make about the operation of the ARQ protocol. [10 marks] 3 [TURN OVER CST.2001.5.4 4 Computer Graphics and Image Processing (a) Describe the limitations of human vision in terms of: (i) spatial resolution (ii) luminance (iii) colour and explain the implications that each of these limitations has on the design of display devices. [10 marks] (b) In image compression we utilise three different mechanisms to compress pixel data: (i) mapping the pixel values to some other set of values (ii) quantising those values (iii) symbol encoding the resulting values Explain each mechanism, describe the way in which it helps us to compress the image, and describe in what way it affects the visual quality of the resulting (decompressed) image when compared with the original. [10 marks] SECTION B 5 Comparative Programming Languages (a) Outline the main innovations that are in Simula 67 but were not in Algol 60, paying particular attention to Simula Classes. [6 marks] (b) Illustrate how Simula can be used to simulate a small restaurant with six tables, two waiters and small groups of customers arriving at random intervals. 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.

Show how you would calculate the first intersection point between an arbitrary ray and a finite length open cylinder of unit radius aligned along the x-axis. [Note: an open cylinder is one which has no end caps.] Having calculated the intersection point, how would you calculate the normal vector? [7 marks] (b) A non-rational B-spline has knot vector [1, 2, 4, 7, 8, 10, 12]. Derive the first of the third order (second degree) basis functions, N1,3(t), and graph it. If this knot vector were used to draw a third order B-spline, how many control points would be required? [7 marks] (c) Describe how an object built using constructive solid geometry (CSG) can be represented using a binary tree. Given the intersection points of a ray with each primitive in the tree, show how to calculate the first intersection point of the ray with the entire CSG object. [6 marks] 2 CST.2000.9.3 5 Business Studies What is meant by a critical path? [5 marks] The village bakery has asked you to advise them about setting up a web site, including a trading function. Draw up a project plan, illustrated by a GANTT chart, and indicate the critical path. [5 marks] Make an estimate of the costs involved, and estimate how much working capital you would need. [5 marks] What other advice would you give them? [5 marks] 6 Security The owner of a banking system which previously used manually distributed shared keys to compute MACs on transactions decides to use public key cryptography to distribute MAC keys in future. The proposed protocol is A B : { {TA, KAB}K1 A KB } Explain the symbolism used in this description. [2 marks] What is wrong with this protocol? [6 marks] The protocol is changed to A B : { {A, TA, KAB}K1 A KB } What attacks might there be on the system now? [12 marks] 3 [TURN OVER CST.2000.9.4 7 Computer System Modelling A database system has a central processor and three (different) discs. Measurements are taken for 1000 transactions on a lightly loaded system and the following observations are made. The CPU scheduler initiated or resumed transaction processing 10,000 times. The total CPU usage was 25 seconds. Disc 1 made 5000 transfers with an average transfer time of 10 ms. Disc 2 made 2000 transfers with an average transfer time of 50 ms. Disc 3 made 2000 transfers with an average transfer time of 20 ms. Derive the visit counts, service times and transaction service demands. What is the bottleneck device? What is the maximum throughput of the system measured in transactions per second? [6 marks] Describe two balanced systems which bound the throughput of the system. What is the maximum throughput of these systems? [7 marks] Recall that the throughput of a balanced system with K devices, N customers and service demand D per device is X(N) = N (N + K 1) 1 D How many transactions do you expect to be in the system with a throughput of 7 transactions per second? [7 marks] 4 CST.2000.9.5 8 Neural Computing Give evidence supporting the view that the main computational load that has shaped the evolution of the human brain is "social computation", with sexual success being the ultimate measure of the value of an algorithm or neural design feature. Say what implications this has for: The cognitive skills and perceptual faculties that have been selected for in brain evolution, as contrasted with the goals which are the traditional focus of AI. The design of face recognition algorithms, which aim to interpret facial expression, gesture, and intent, as well as gender and identity. The construction of the theory that other persons have minds, too. Models of action, planning, and interaction between self and others. [8 marks] Comment on whether this "social computation" view of human brain evolution implies that brain science is less relevant to the goals of computer science than is usually thought. [2 marks] Answer any five of the following seven short questions: (a) Roughly what is the total number of neurones in the human brain? (b) Roughly what is the total number of synapses in the human brain? How does this compare with the total number of stars in our galaxy, and with the total number of galaxies in the known universe? (c) Why is nerve impulse propagation described as "saltatory", and what purposes are achieved by this method of signalling? (d) What is the approximate speed of nerve impulse propagation in warm-blooded animals, in metres/sec? (e) Why is "white matter" white, what cells are responsible for this, and what purpose do they serve?

Consider a language J which has Java-like syntax nested definitions of procedures within other procedures local variables (with static binding) raising and handling of named, parameterless exceptions Explain a possible run-time data structure which a compiler for J might use.

A nave user of such a language suggests that the resultant compiled code will spend a significant fraction of execution time searchingboth finding the store location corresponding to the use of a variable name and finding the exception handler corresponding to the raising of a given exception name. Determine with justification whether this is so for your run-time data-structure proposed above. [4 marks] Now instead suppose a simple interpreter for J is written, so that searches for variable (or exception) names search the appropriate environment for the variable value or exception handler code. To what extent are these searches bounded by (a) the number of variables or exceptions in the program or (b) the dynamic or static nesting of procedures? [6 marks] 7 Prolog for Artificial Intelligence Consider the following Prolog program, which is intended to define the third argument to be the maximum value of the first two numeric arguments: max(X, Y, X) :- X >= Y, !. max(X, Y, Y). (a) Provide an appropriate query to show that the above program can give an incorrect result. [4 marks] (b) Explain the cause of the error. [6 marks] (c) Suggest a correction. [5 marks] (d) Write a Prolog program to find the maximum of a list of numbers.

Describe the use of a table of pointers and a table of extents to store the list of disc blocks which compose a file. Pay particular attention to how such data structures can be designed to enable the efficient support of very large files, and give estimates of their performance for finding the location of a block chosen at random. [14 marks] Describe how such data structures would be used in the implementation of a log-structured file system with consideration of the impact of garbage collection. [6 marks] 5 UNIX Case Study For the UNIX operating system, define (a) process [2 marks] (b) the execution environment of a process [3 marks] (c) the fork system call [3 marks] Explain how a command line of the form given below is implemented: command & [9 marks] Outline the essential difference in the implementation of command lines of the form given below: command1 & command2 command1 | command2 [3 marks] 6 Data Structures and Algorithms Give an algorithm which selects the median value from an array of n values explaining how the possible execution time depends on n. (You should clarify the word "possible".) [10 marks] Describe two tests. The first should determine whether two line segments intersect. The second should determine whether a given (half-infinite) straight line from a point (x, y) in the direction (u, v) [thus the points on the line are (x + u, y + v) for > 0] intersects a given polygon other than at a vertex. [10 marks] 3 [TURN OVER CST.94.11.4 7 Distributed Systems Explain the importance of ensuring the timeliness of messages in cryptographic protocols. [8 marks] Give a careful account of the main techniques used for ensuring timeliness, including any environmental assumptions. Under what circumstances is it proper to use time values when there is no clock synchronisation? [12 marks] 8 Graphics Describe the method of Douglas & Pucker for approximating one line chain by another to within some tolerance. Are there any special cases? [20 marks] 9 Numerical Analysis I With reference to a decimal floating-point implementation with 4-digit precision ( = 10, p = 4), describe the two most common methods of rounding. (Use 1.2345 and 1.2375 as examples.) Which method is unbiased? [3 marks] What do you understand by the terms machine epsilon, and guard digit? [4 marks] Suppose the largest representable floating-point number is about 1050, and consider evaluation of p x 2 y 2. How would you compute the result? (Use x ' 5.1040 , y ' 3.1040 as an example.) How could your method also improve accuracy on some machines?

(a) Explain how to describe the structure of a collection of data using entities, attributes and relationships. [6 marks] (b) How would you identify particular instances of data in order to record the information in a database? Illustrate your answer by considering both a relational database maintained using SQL-92 and an ODMG database. [6 marks] (c) A high street bank has just announced a merger with a nationwide building society. You are employed as a consultant to advise on the integration of their client databases. Both institutions use relational databases. Write brief notes to alert the database administrators to the difficulties that they may encounter.

Discuss capability-based access control under the headings protection of capabilities control of transfer of capabilities between principals delegation of rights revocation of capabilities Your answer should mention the differences between the management of capabilities in distributed as opposed to centralised systems. You should consider alternative designs of capabilities. [20 marks] 2 Digital Communication II What is a leaky bucket algorithm? How can it be used to police traffic? How can it be used to shape traffic? [5 marks] You are required to provide a flow admission controller for a router. RSVP is used to request resources for flows with leaky bucket parameters. Outline how you would design the controller, bearing in mind the soft state nature of RSVP.cess with mean rate , and processes customers at a mean rate of .

: Write Java program to read a file content line by line and then print the content as console output

(a) What are the distributions and parameters of the inter-arrival and service times of customers? [3 marks] (b) Sketch an outline proof showing that the distribution of the departure process from the queue is the same as that of the arrivals process. [10 marks] Briefly contrast analytical queueing analysis and discrete event simulation with regard to their fields of applicability and other important considerations for the systems modeller. [7 marks] 4 VLSI Write short notes on two of the following: (a) the fundamental limits which may slow down progress in semiconductor technology; (b) designing VLSI systems for low-power applications; (c) problems which can prevent an apparently properly designed chip from working to specification. [10 marks each] 2 CST.98.9.3 5 Business Studies You are assigned the role of UK sales and marketing manager for a new kind of low-cost computer, primarily aimed at the educational market. Whilst not directly PC compatible, the computer includes web access, PC-compatible word processing, other PC-compatible productivity tools, and a suite of educational programs. How would you approach this task? Draw up an outline business plan as follows. (a) Show what communication and distribution channels you propose. [5 marks] (b) Propose a selling price, and estimate the number of units you might sell at this price. [5 marks] (c) Estimate a 3-year budget for the sales and marketing activity. [5 marks] (d) State how you would refine your estimates, and what monitoring you would put in place. [5 marks] Background information: There are about 32,000 schools in the UK. The UK government has recently published a consultative document The National Grid for Learning with a proposal to spend 100M on provision of internet access in schools over the next 5 years. This sum includes infrastructure provision, content development and teacher training, as well as a contribution to provision of computers in schools. The average school IT spend is projected to be 18,000 each year. Additional funding may be available from government and parents for specific projects. The unit manufacturing cost is 200, delivered