Describe, in outline, each of the implicit surface, NURBS surface, and constructive solid geometry methods for defining three-dimensional shapes. (b) Compare and contrast the three methods. (a) Describe the congruential methods for generating pseudo-random numbers from a Uniform (0, 1) distribution. [3 marks] (b) Let U be a Uniform (0, 1) random variable. Show that for any continuous distribution function, F(x), the random variable, X, defined by X = F 1 (U) has the probability distribution function F(x). [3 marks] (c) Apply the method of part (b) to generate random variables with the following distributions. In each case, specify the distribution function F(x) that you use. (i) Uniform distribution on the interval (a, b), for a < b. (ii) Exponential distribution with parameter . (d) Define the Poisson process, N(t), (t 0) of rate . (e) Show that for each fixed t 0, N(t) is a Poisson random variable with parameter t. (f ) Show that the interarrival times of consecutive events in a Poisson process of rate are independent random variables each with the exponential distribution with parameter . Show how this leads to a method to simulate the events of a Poisson process. (a) What is total about total correctness? [2 marks] (b) State the WHILE-Rule of Floyd-Hoare Logic. [2 marks] (c) Give a proof of {T} }. [2 marks] (d) What does the truth of {T} (e) How are expressions like 1/0 handled in Floyd-Hoare Logic? complete (f ) What are verification conditions? (g) Must the verification conditions be true for correctness? Briefly justify your answer. (h) Name one method used to prove verification conditions. [2 marks] (i) What are the "hooked" variables in VDM used for? (j) What are weakest preconditions and weakest liberal preconditions?

answer everything

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. it is well. (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.

What is temporal abstraction? How are models at different temporal abstraction levels related? [4 marks] (c) What is the difference between LTL and CTL? [4 marks] (d) How do the Verilog and VHDL simulation cycles differ? [4 marks] (e) What is the difference between formal verification using model checking and using theorem proving?

Information retrieval systems vary in the expressivity of the query languages they employ. For instance, some systems support proximity search: if two query terms are connected by the "Next" operator, then only those documents are retrieved where the query terms appear close together (i.e., within a certain number of words of each other). (a) List and briefly describe other ways in which the syntax and the interpretation of query languages may vary. [8 marks] (b) Describe with an example how the "Next" operator described above is implemented efficiently in modern information retrieval systems. Your answer should include a description of the data structure(s) necessary to support it. [5 marks] (c) A search engine supports error correction in the following way: If an error is suspected in a query term, the system provides a link labelled "Did you mean X?", where X is the corrected term, in addition to its normal results. The link leads to a list of retrieved documents, corresponding to a variant of the original query, with X replacing the misspelled term. (i) Explain why it is non-trivial to implement this feature efficiently. [3 marks] (ii) Discuss methods for implementing this feature in a realistic setting. [4 marks] 8 CST.2006.7.9 12 Natural Language Processing The following shows a simple context free grammar (CFG) for a fragment of English. S -> NP VP Adj -> angry Vbe -> is VP -> Vbe Adj Adj -> big N -> dog NP -> Det N Adj -> former N -> cat N -> Adj N P -> at Adj -> Adj PP P -> on PP -> P NP Det -> the (a) Show the parse tree that this grammar would assign to (1). (1) the dog is angry at the cat [3 marks] (b) One respect in which this grammar overgenerates is that some adjectives, including former, occur only before a noun (see (2)) and that PPs do not combine with adjectives occurring before a noun (see (3)). (2) * the dog is former (3) * the angry at the cat dog is big Show how the grammar given above could be modified to prevent this type of overgeneration. [4 marks] (c) The grammar also behaves incorrectly with examples (4), (5) and (6): (4) * the dog is big at the cat (big does not take a PP) (5) * the dog is angry on the cat (angry only takes PPs where the P is at) (6) * the dog is angry at the cat at the cat (adjectives may not combine with multiple PPs) Show modifications to the grammar which would prevent these types of overgeneration. [5 marks] (d) Describe how the overgeneration in part (c) could be dealt with in a feature structure (FS) grammar, giving full lexical entries for angry and big and details of rules and other lexical entries as necessary to explain your account. [8 marks] 9 (TURN OVER) CST.2006.7.10 13 Business Studies (a) Name five different types of intellectual property. [5 marks] (b) Distinguish between "Deep linking" and "Direct linking". Can a search engine deep link without infringing the copyright of the original site? [5 marks] (c) Why is the use of thumbnails of pictures by a search engine fair use? [5 marks] (d) Why are there likely to be only a few dominant search engines? [5 marks] 14 E-Commerce (a) In a telecommunications business context, what is meant by Triple and Quadruple Play strategies, and what will be the effects of the adoption of such strategies? [10 marks] (b) Describe possible business models for a small independent Internet television start-up company. Estimate start-up costs and profitability, and describe some of the challenges such a television station will need to overcome. [10 marks] 10 CST.2006.7.11 15 Additional Topics (a) (i) Briefly describe the purpose of broadband fixed wireless access (FWA) and give typical situations where it could be deployed. [4 marks] (ii) What advantages does radio offer over traditional wired access? [2 marks] (b) Explain how intersymbol interference (ISI) arises in a wireless communication system and its effect on system performance. [2 marks] (c) (i) Describe how linear equalisation orthogonal frequency division multiplexing (OFDM) can be used to combat ISI. [4 marks] (ii) Highlight a problem which can occur when using linear equalisation and describe an alternative equalisation approach that can overcome this problem. What problem can occur with this alternative approach? [4 marks] (iii) Highlight problems that arise with the use of OFDM. In what situation is OFDM preferred over the use of equalisation? [4 marks] 11 CST.2006.7.12 16 Additional Topics (a) What is an (m, M)R-Tree? Explain how new items can be inserted and how range queries can be evaluated. [6 marks] (b) Explain the trade-off in varying m between small and large values. If the dataset is known in advance, would a large or small value of m be appropriate? [4 marks] (c) R+-Trees, R -Trees, and QSF-Trees are special forms of R-Tree. Explain how each differs from the basic R-Tree and what advantage is presented by each modification. [2 marks each] (d) As private motor cars increase in electronic sophistication, Sentient Computing becomes ever more applicable. Describe two context-aware behaviours that a car's electronic systems could exhibit, making use of general-purpose processing power, data storage, and wireless data communication. [2

(a) Give three different expressions for mutual information I(X; Y ) between two discrete random variables X and Y , in terms of their two conditional entropies H(X|Y ) and H(Y |X), their marginal entropies H(X) and H(Y ), and their joint entropy H(X, Y ). Explain in ordinary language the concept signified by each of the measures H(X|Y ), H(X), H(X, Y ), and I(X; Y ). Depict in a Venn diagram the relationships among all of the quantities mentioned here. [8 marks] (b) Suppose that women who live beyond the age of 70 outnumber men in the same age bracket by three to one. How much information, in bits, is gained by learning that a certain person who lives beyond 70 happens to be male? (d) If we wish to increase the transmission capacity of a noisy communication channel, is it more effective to increase its electronic bandwidth in Hertz, or to improve its signal-to-noise ratio? Briefly say why. [2 marks] (e) A continuous signal whose total bandwidth is 1 kHz and whose duration is 10 seconds may be perfectly represented (even at points in between the points at which it is sampled) by what minimal number of real numbers? [2 marks] (f ) Give the names of three functions (not necessarily their equations) which are self-Fourier

Describe how a data model is represented in a relational database, and explain how one might specify a relational database schema. [5 marks] What is meant by a referential integrity constraint in a relational database? [3 marks] Each year the number of tourists coming to Cambridge increases by 10%. Most of the pressure falls on a limited number of identified sites in the city centre. The Tourist Board has restricted the size of any group visiting such a site to 20, and requires a group of ten people or more to get a permit in advance. Most bookings are made either by tour operators or directly by independent guides: the Tourist Board will arrange guides for groups if asked to do so. A database is being installed to coordinate bookings and to provide information about the opening times of sites. Each site has separate opening times for summer and winter (owing to college autonomy, changes of season differ from site to site). Permits are issued to start on the hour or on the half-hour: they are valid either for 1 hour or for 2 hours, the duration being fixed for each site. The final permits of each day are timed to expire at the site's closing time. Each site has a fixed capacity, and no booking can be accepted that would cause it to be exceeded. The charge for a permit depends only on the site and the season. (Occasionally sites are closed for several hours during the normal opening period, for example when recording is taking place in King's College Chapel. The protocol is to inform the Tourist Board at least 6 months in advance.) The Tourist Board issues permits to visit an identified site at a given time on a given day, specifying the booking agent and the number in the group. Bookings can be made up to 6 months beforehand. Permits are issued to registered tour operators and guides on account, but in all other cases payment must be made in advance. The data held for registered guides includes not only account details but also their working hours and charges. Design a schema for the relational database that is to record this information for the Tourist Board. You may find it helpful to use domain types DATE, TIME and MONEY in addition to standard programming language datatypes. You do not need to specify the transactions that maintain the database, but you should state clearly any assumptions that influence the schema design.

Write Java program to read a character and push the character on to the stack a Java program to read two data items and print their sum, difference, product, and quotient.

Discuss the problems of providing tractable models of transistors suitable for hardware verification by formal proof. Compare and contrast at least two different models. Illustrate your discussion with concrete examples of transistor circuits. [20 marks] 10 Complexity For each of the following statements state whether the claim made is true, false or if more information is needed before a judgement can be made. Give one-sentence justifications of your assertions. (a) Sorting a list of numbers into ascending order is an NP problem. (b) Sorting a collection of programs into order so that the ones that finish quickly come before those that run for a long time is an NP-complete problem. (c) To be NP-complete is to be as difficult as any solvable problem can be. (d) Any NP problem can be solved (on an ordinary computer) in polynomial space and exponential time. (e) The problem of determining whether a k-clique is present in a graph is known to be NP-complete. Therefore for large graphs and large values of k it will always be impossible (in practice) to find such a clique even if it is known that one exists. (f ) For the purposes of complexity theory each of the cost functions n log n, n 1.573 and n! counts as polynomial growth. [20 marks] 11 Computation Theory Explain Turing's Thesis. [5 marks] (a) What is meant by saying that a Turing machine has searching states? Show that any Turing machine computation can be effected by a machine with searching states, equivalent in the sense that the head movements are identical and the same symbols are written to the tape. [5 marks] (b) Show that, subject to suitable encoding, any computation can be carried out by a Turing machine having only two states.

Discuss the relations among the following concepts: (a) secrecy (b) confidentiality

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

Consider a noiseless analog communication channel whose bandwidth is 10,000 Hz. A signal of duration 1 second is received over such a channel. We wish to represent this continuous signal exactly, at all points in its one-second duration, using just a finite list of real numbers obtained by sampling the values of the signal at discrete, periodic points in time. What is the length of the shortest list of such discrete samples required in order to guarantee that we capture all of the information in the signal and can recover it exactly from this list of samples? Name, define algebraically, and sketch a plot of the function you would need to use in order to recover completely the continuous signal transmitted, using just such a finite list of discrete periodic samples of it. Consider a noisy analog communication channel of bandwidth , which is perturbed by additive white Gaussian noise whose power spectral density is N0. Continuous signals are transmitted across such a channel, with average transmitted power P (defined by their expected variance). What is the channel capacity, in bits per second, of such a channel?