Help solve these networking queries Consider the task of…Help solve these networking queries Consider the task of determining whether a given word (a string) can beexpressed by joining together various chunks (non-empty strings). If thechunks are abra, cad and hal, then the word abracadabra can be expressedas abra|cad|abra. Note that if the available chunks are ab, bra, cad and abra,then the first two are no good for expressing abracadabra, and yet a solutioncan be found using cad and abra. The chunks can be used any number of timesand in any order.Write code for a function that takes a list of chunks along with a word, andreturns a list of chunks that yield the word when concatenated. For the examplesabove, the result should be [“abra”, “cad”, “abra”]. Exception Fail shouldbe raised if no solution exists. [10 marks]Note: You are given a function delPrefix for removing an initial part of a string.For example, delPrefix (“abra”, “abracadabra”) returns “cadabra”, butdelPrefix (“bra”, “abracadabra”) raises exception Fail.All ML code must be explained clearly and should be free of needless complexity.Well-known utility functions may be assumed to be available. (a) Explain how each number e ? N can be decoded uniquely as a register machineprogram Probe. [6 marks](b) What would it mean for a register machine to decide the halting problem?[4 marks](c) Prove that such a register machine cannot exist. (You may assume theexistence of suitable register machines for copying registers and manipulatinglists of numbers so long as you specify their behavior clearly.) [10 marks]11 Numerical Analysis I(a) Consider a version of the Brown model in which the significant of a floating point number is represented as d0.d1d2 . . . dp-1. Explain the parameters ß, p,emax, emin of the model. [3 marks](b) Describe the layout of bits in IEEE single precision and give the values of theabove four parameters. [5 marks](c) IBM System/370 single precision uses the same total number of bits, anda similar method for storing negative exponents. However, there are 7 bitsfor the exponent, and all bit patterns represent numbers. Given ß = 16,deduce the values of the remaining three parameters for this floating-pointimplementation. (d) If ß = 10, p = 3 how should 6.789, 6.785, 6.755 be rounded using the “roundto even” method? [3 marks](e) Now consider ß = 2, p = 8 on a machine with just one guard digit. Howshould the following be rounded using “round to even”? (a) If you had been one of the original inventors of the WIMP interface, and engineers on the technical team had been sceptical about the advantages that it would bring, then:(i) What two pieces of empirical evidence could you have presented to sceptics to help convince them? [2 marks](ii) Describe the technique that you would use to collect data for each of these. [4 marks](iii) Describe the technique that you would use to analyse each of those data sets. [4 marks](b) If you were the HCI researcher on a speech interaction project intended to replace the WIMP interface, then(i) Which of the techniques described above would be most relevant to your work? Why? [3 marks](ii) Explain how a modern analytic evaluation method could give design guidance to the team, including a description of how the analysis would be conducted, and two design improvements that might result from that analysis. [7 marks](a) Sketch designs for an n-input NAND gate in CMOS using(i) static CMOS;(ii) dynamic CMOS;(iii) pseudo-nMOS. [2 marks each](b) Assuming that a conducting p-channel has a resistance ? times that of a similarly sized n-channel, annotate each of your circuit diagrams with suitable widths for the transistors, and explain the reasons for their values. [2 marks each](c) For each design, calculate the logical eort and the parasitic delay. [2 marks each](d) Which is likely to be fastest for the case when n = 4 and ? = 3? What dierence would it make if the circuit were driving a large capacitative load? [2 marks]3 Optimising CompilersAssume that a program consists of a sequence of declarations Object o; where o is an object name, followed by a sequence of function denitions f(x1,…,xk) = e where expressions, e, have syntaxe ::= n | o | x | f(e1,…,ek) | let x = e1 in e2 | if e1 then e2 else e3. where n ranges over integer constants and x over variables (which may contain integers or object references). Variables may not contain function values.Alias Analysis is a technique which will determine that, during evaluation of e within let x = o in let y = o in ex and y alias because they are both references to the same object o.(a) Show how to associate a ow variable with each variable and (sub-)expression of the program. State the values which ow variables might reasonably take in such an analysis. [4 marks](d) Explain how you would respond to the criticism that your analysis may fail to terminate if your language is extended with arithmetic expressions because a single expression may give rise to an innite set of values. [2 marks](e) Briey describe any optimisation whereby knowing that x and y cannot alias is necessary for the optimisation to be safe. [2 marks](a) The mid-point rule can be expressed in the form In =Z n+ 1 2 n-1 2 f(x)dx = f(n) + enwhereen = f00(?n)/24 for some ?n in the interval (n-1 2,n+ 1 2). Assuming that a formula forRf(x)dxis known, and using the notationSp,q =q X n=pf(n) ,describe a method for estimating the sum of a slowly convergent series S1,8, by summing only the rst N terms and estimating the remainder by integration. [5 marks](b) Assuming that f00(x) is a positive decreasing function, derive an estimate of the error |EN| in the method. [5 marks] (c) Given Z dx (1 + x)vx = 2tan-1vx illustrate the method by applying it to8 X n=11 (1 + n)vn .Verify that f00(x) is positive decreasing for large x, and estimate the integral remainder to be added to S1,N. [6 marks] (d) How large should N be to achieve an absolute error of approximately 2×10-15? [You may assume N + 1 ‘ N for this purpose.] [4 marks]9 Mathematics for Computation Theory(a) Prove Arden’s Rule for events, that X = A*B is the least solution of the inequality X > B + AX. [6 marks] (b) Let M =A B C Dbe a (2×2) event matrix. Show that the matrix Y = (A + BD*C)* A*B(D + CA*B)* D*C(A + BD*C)* (D + CA*B)*satises the equation Y = I + MY . [4 marks](c) The deterministic nite automaton M has a 2-symbol alphabet {a,b}, and a single accepting state a, the initial state. The transition diagram is as follows:b aaabbaß?Show that the event accepted by M can be denoted by the regular expression[a*b(a a*b)*b]*[10 marks](a) Explain what is meant by the following statements: (i) f : N?N is a total recursive (TR) function; [3 marks] (ii) the sequence {fn : N ? N}n?N of TR functions of a single variable is recursively enumerable. [4 marks](b) Show that no recursive enumeration can include the set of all TR functions of a single variable. [4 marks](c) Suppose u(n,x) is a recursive enumeration of the sequence of TR functions fn(x) = u(n,x). Show how to dene a sequence {gn : N ? N} of TR functions of a single variable such that each gn is distinct from every function fn, and also from each gk for k 6= n. [5 marks] (d) Express the sequence {gn} as an explicit recursive enumeration v(n,x) = gn(x). [4 marks]11 Software Engineering and Design(a) Compiler development is sometimes cited as an example of a situation in which the waterfall model should be applied. Why is this? [2 marks](b) Imagine that a user-centred design model were applied to the development of programming language products instead. Discuss what might happen dierently during the development of those products. [8 marks](c) Suggest two design innovations that might result from the new approach. Draw a UML diagram to illustrate each of those designs, using a dierent kind of diagram in each case. [10 marks]A software project has two phases, each with three tasks. They are expected to take the following amount of eort:Phase 1: Analysis: 3 weeks Code: 2 weeks Test: 1 weekPhase 2: Analysis: 1 week Code: 2 weeks Test: 3 weeksWithin a phase a task cannot start until the previous task completes. A task in Phase 2 cannot start until the corresponding task in Phase 1 has completed.(a) Draw the PERT and Gantt charts for the project. What is the minimum elapsed time? [5 marks](b) Two sta are assigned to the project, an analyst and a programmer. The analyst also acts as test engineer. How long will the project take with this stang? [5 marks] Write program to check that your student id isEven or oddPrime numberWrite program to check that your student id isEven or oddPrime number (a) Describe an algorithm which draws a Bezier cubic curve to a specified toleranceusing straight lines. [7 marks](b) Describe an algorithm for clipping a line against a rectangle. (c) A Bezier cubic curve could be clipped and drawn using the algorithm in (a)to produce straight lines and the algorithm in (b) to do the clipping. Describea more efficient algorithm which draws a Bezier cubic curve clipped against arectangleJava generics allows an ArrayList object to be constrained to use a single specifictype (e.g. ArrayList