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Rewrite the grammar to eliminate ambiguity. [4 marks] (c) Transform…Rewrite the grammar to eliminate ambiguity. [4 marks](c) Transform the grammar of part (b) into an equivalent one that could be usedfor recursive descent parsing. Explain your answer. [5 marks](d) Write  a recursive descent parser for your grammar. [9 marks]4 Business Studies(a) Name five different types of intellectual property. [5 marks](b) Distinguish between “Deep linking” and “Direct linking”. Can a search enginedeep 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]4CST.2006.11.55 Artificial Intelligence I(a) Give a brief description of the way in which if-then rules can be used as a basisfor knowledge representation and reasoning. What essential elements wouldyou expect to be included in such a system? [3 marks](b) In the context of such a system, give detailed descriptions, illustrating youranswers with specific examples, of the following concepts:(i) pattern matching; [2 marks](ii) reason maintenance; [2 marks](iii) forward chaining; [4 marks](iv) conflict resolution strategies; [4 marks](v) backward chaining with backtracking. [5 marks]6 Operating System Foundations(a) (i) Define a scheduling algorithm based on multilevel feedback queues.[6 marks](ii) Discuss the properties of your algorithm. Where appropriate, outlinedifferent design decisions that could have been taken. [6 marks](b) Discuss the implications of an operating system supporting(i) single-threaded processes only;(ii) multi-threaded processes. [8 marks]5 (TURN OVER)CST.2006.11.67 Numerical Analysis I(a) The Newton-Raphson iteration for solution of f(x) = 0 isx˜ = x -f(x)f0(x).By drawing a carefully labelled graph, explain the graphical interpretation ofthis formula. What is the order of convergence? [4 marks](b) Consider f(x) = x3 + x2 – 2. The following table shows successive iterationsfor each of the three starting values (i) x = 1.5, (ii) x = 0.2, (iii) x = -0.5.Note that, to the accuracy shown, each iteration finds the root at x = 1.n (i) (ii) (iii)0 1.50000×1002.00000×10-1-5.00000×10-11 1.12821×1003.95384×100-8.00000×1002 1.01152×1002.57730×100-5.44318×1003 1.00010×1001.70966×100-3.72976×1004 1.00000×1001.22393×100-2.56345×1005 1.00000×1001.03212×100-1.72202×1006 1.00079×100-9.62478×10-17 1.00000×1001.33836×1008 1.00000×1001.06651×1009 1.00329×10010 1.00000×10011 1.00000×100Sketch the graph of f(x) and show the first iteration for cases (i) and (ii)to show why (i) converges faster than (ii). In a separate sketch, show thefirst two iterations for case (iii). [Hint: a very rough sketch will suffice forcase (iii).] [10 marks](c) Now consider f(x) = x4 – 3×2 – 2. Calculate two Newton-Raphson iterationsfrom the starting value x = 1. Comment on the prospects for convergence inthis case. [6 marks]6CST.2006.11.78 Mathematics for Computation Theory(a) What is a deterministic finite automaton (DFA) over the finite alphabet S?[2 marks](b) Define the event E accepted by the DFA M over S. [3 marks](c) State Kleene’s Theorem, which characterises the algebraic structure of eventsthat are accepted by some DFA. [3 marks](d) Design a DFA over S = {a, b} that accepts precisely those strings ending in bthat do not contain two successive occurrences of a. [4 marks](e) Give an algebraic specification of the event, proving that your expression hasthe required properties. [8 marks][You may if you wish assume that if M =A BC D is a partitioning of thetransition matrix of a DFA so that A and D are square, thenM* =(A + BD*C)* A*B(D + CA*B)*D*C(A + BD*C)* (D + CA*B)*with the same partitioning.]9 Computation Theory(a) Define the collection of primitive recursive functions. [6 marks](b) Why is a primitive recursive function always total? [1 mark](c) Show that the function m from N2to N given bym(x, y) = x – y if x = y0 if x < yis primitive recursive. [3 marks](d) Define the collection of partial recursive functions. [3 marks](e) What is meant by a total recursive function? [1 mark](f ) Show that there exist total recursive functions that are not primitive recursive.Any standard results about register machines or recursive functions that youuse need not be proved, but should be clearly stated. [6 markImage transcription text6. [5 points each] (a) Is 2 a primitive rootof 11? (b) Find the discrete logarithm of3 modulo 11 to the base 2. … Show more… Show more Image transcription text(d) Decrypt the ciphertext messageLEWLYPLUJL PZ H NYLHA ALHJOLYthat was encrypted with th… Show more… Show more  Computer Science Engineering & Technology NetworkingCSCI 1301

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