Compiler Construction (a) Give two motivations behind why a compiler is ordinarily separated into passes (or stages) and demonstrate a commonplace arrangement of passes and the information structures passed between them (b) and run inside numerous programs, could vary from that of accumulating an application and running it on various occasions on a solitary machine. B ::= Leaf | Br (n, B, B) where n ranges over regular numbers. Albeit this question concerns the encoding of double trees as ?-terms, you might utilize the encodings of other notable information structures, for example, booleans and matches, gave you express the properties accepted. Give an encoding of twofold trees as ?-terms by characterizing as ?-terms (a) Leaf and Br, used to develop the ?-terms comparing to parallel trees; (b) is Leaf, which tests whether a ?-term relates to a leaf or a branch hub; (c) esteem, fstsubtree and sndsubtree, used to recognize separately the normal number and the two subtrees at a branch hub. Legitimize your response by portraying the way of behaving of is Leaf, esteem, fstsubtree and sndsubtree: for instance, the decrease isLeaf(Leaf) genuine depicts part of the way of behaving of isLeaf. [8 marks] Consider the capacity tree add characterized inductively on the construction of double trees by treeadd (m, Leaf) = Leaf treeadd (m, Br (n, B1, B2)) = Br (m + n,treeadd (m, B1),treeadd (m, B2)) Give and legitimize a ?-term which encodes treeadd, utilizing the ?-term Y ? ?f.(?x.f(xx))(?x.f(xx)). [6 marks] Give the ?-term for the limitless paired tree whose branch hubs comprise of zeros at even profundities and ones at odd profundities, as presented underneath: 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 . . . [6 marks] 7 [TURN OVER CST.98.6.8 10 Logic and Proof Outline the ideas driving modular rationale. Delineate your response by making sense of the importance of the saying A ? tu A. [6 marks] Attempt to demonstrate, involving rules for S4, the accompanying sequents: tu(A ? B) ? (tuA) ? (tuB) (tuA) ? (tuB) ? tu(A ? B) For each sequent, momentarily make sense of why it is legitimate (or isn't, by and large). [4 + 4 marks] Use goal to get an inconsistency from this arrangement of provisions: {P(x, x), P(x, a)} {P(x, x), P(x, f(a))} {P(y, f(x)), P(y, x)} [6 marks] 8 CST.98.6.9 11 Complexity Theory Here are a few casually offered viewpoints about computational intricacy. They might be right, wrong, deceptive or inane. In some

cases reality or in any case of the assertion probably won't be known, either in that frame of mind of it not having been shrouded in the course or by the response not being known by anyone anyplace. For every assertion remark on its legitimacy and in situations where that is both fundamental and clear produce a changed adaptation of the perception that is appropriately substantial. You are not supposed to incorporate confirmations to help your cases. (a) Problems that are not NP-re simple to tackle. [3 marks] (b) Problems that are NP-finished won't ever be tackled in that frame of mind of time despite the fact that PCs keep on getting quicker and quicker. [3 marks] (c) To test a number N to see whether it is prime you simply need to do testdivision by every one of the numbers from 2 to N ? 1, and since there are just N ?2 of these and division should be possible in time O(n 2 ) this is polynomial time. Along these lines primality testing is in the class P. [4 marks] (d) There is a polynomial-time decrease from the k-inner circle issue to 3-SAT. [3 marks] (e) There is a polynomial-time decrease from 3-SAT to the k-inner circle issue. [3 marks] (f ) There have been proposition that organic PCs in light of DNA could utilize the monstrous parallelism of their biochemical movement to quickly tackle NP issues. In the event that such frameworks could be made to work dependably this would tackle the hypothetical test presented by the idea of NP-fulfillment. [4 marks] 9 [TURN OVER CST.98.6.10 12 Semantics of Programming Languages What is implied by a named progress framework? [2 marks] A language of orders, C, for intuitive info/yield is given by C ::= skip | ' := ' | getc(') | putc(') | C ; C | in the event that ' = ', C else C | while ' = ' do C where ' ranges over some decent arrangement of areas for putting away characters. The order '1 := '2 duplicates the items in '2 to '1. The order getc(') peruses the following person from the standard information stream into '. The order putc(') composes the items in ' to the standard result streamFrame the information structures held by the working framework. [5 marks] Describe the activities of the working framework because of a location special case because of not matching the location gave by the processor in the TLB. [5 marks] How might the working framework at any point utilize access consents to help its page substitution strategy? [4 marks] 8 Data Structures and Algorithms A coordinated chart of n hubs numbered 1, 2, . . . , n can be addressed by a n n nearness lattice G1, where G1[i, j] is valid assuming there is an edge interfacing hub I to hub j, and G1[i, j] is misleading in any case. Likewise, characterize Gk to be that framework with the end goal that Gk[i, j] is valid assuming there is a way of length 6 k interfacing hub I to hub j, and Gk[i, j] is misleading in any case,

Problem 3: Find and display the values of both sides of the following mathematical series expression and an absolute difference of both sides. User can input either of angles in degree 90, 60, 30 etc. sin(x) = x - 3! 5! 9! Once the user enters the angle in degrees. Your program should do the following (Write separate functions for a, b, c, and d) a) LHS Result b) RHS Result c) Difference d) First term, series of two terms, series of three terms, series of four terms, series of five terms. Problem 4: A car completes its journey in three parts. It travels the first X km of its journey at an average speed of x_Speed m/s and the next Y km at an average speed of y_Speed km/h. The car completes the last part of its journey at an average speed of z_Speed km/h in z_Minutes minutes. Here X, x_Speed, Y, y_ Speed, z_Speed, and z_Minutes are all variables whose values you will have to take as an input from the user. Find the average speed for its entire journey, giving your answer in km/h. distance speed = time Hint: First try to solve this problem by assuming / assigning different values to these variables. Make sure that you consider units mentioned with these variables