There are three lawful offense techniques for moving a tile, each with a connected charge: slide into the abutting void region - esteem 1 get around one tile into the vacant region - esteem 1 jump over tiles into the vacant area - esteem 2 The design is to have every one of the white tiles to one side of the dark tiles in general and to obtain this at insignificant worth. The last capacity of the vacant space isn't fundamental. (a) Represent the issue the utilization of the accompanying aptitude portrayal plans: (I) creation framework rules [5 marks] (ii) a semantic organization [5 marks] In one sentence, depict the select accentuations of those two plans. [1 mark] (b) State practical heuristics to help cure this difficulty. [2 marks] (c) For an organizer to tackle this riddle, what administrators (i.E. Arranging moves) could be required?

7 Operating System Functions

(a) with regards to virtual memory the executives:

(I) What is request paging? How could it be executed? [4 marks]

(ii) What is implied by transient area of reference? [2 marks]

(iii) How does the suspicion of worldly territory of reference inflfluence page

substitution choices? Delineate your response by brieflfly depicting an

suitable page substitution calculation or calculations. [3 marks]

(iv) What is implied by spatial area of reference? [2 marks]

(v) In what ways does the presumption of spatial territory of reference inflfluence

the plan of the virtual memory framework? [3 marks]

(b) An understudy proposes that the virtual memory framework ought to manage

"items" or "techniques" as opposed to with pages. Make contentions both for

furthermore, against this idea. [4 and 2 imprints respectively]

.

6CST.2001.4.7

8 Computation Theory

(a) Defifine definitively what is implied by the accompanying:

(I) f(x1, x2, . . . xn) is a Primitive Recursive (PR) capacity of arity n.

[5 marks]

(ii) f(x1, x2, . . . xn) is a Total Recursive (TR) capacity of arity n. [3 marks]

(b) Ackermann's capacity is defifined by the accompanying recursive plan:

f(0, y) = S(y) = y + 1

f(x + 1, 0) = f(x, 1)

f(x + 1, y + 1) = f(x, f(x + 1, y))

For fifixed n defifine

gn(y) = f(n, y).

Show that for all n, y ? N,

gn+1(y) = gn(y+1)(1),

where h(k)(z) is the consequence of k rehashed utilizations of the capacity h to introductory

contention z. [4 marks]

(c) Hence or in any case show that for all n ? N, gn(y) is a PR work. [4 marks]

(d) Deduce that Ackermann's capacity f(x, y) is a TR work. [3 marks]

(e) Is Ackermann's capacity PR? [1 mark]

7

[TURN OVERCST.2001.4.8

9 Numerical Analysis I

(a) What is implied by a symmetric positive defifinite lattice ? [3 marks]

(b) Verify that A = 2 1

1 2 is positive defifinite. [4 marks]

(c) The Choleski factorisation A = LDLT is to be applied to the arrangement of

. Structure the

upper three-sided arrangement of conditions expected to finish the arrangement.

[4 marks]

(d) Solve these conditions. [2 marks]

(e) What is implied by the request for intermingling of an iterative interaction? [1 mark]

(f ) State the Newton-Raphson equation for settling f(x) = 0 for scalar x. What is

the request for combination of this technique? [2 marks]

(g) This technique is utilized to tackle f(x) = x2 ? 4 = 0 utilizing IEEE Double Precision

with a specific beginning worth x0. It is observed that the third emphasize x3 ' 2.0006,

also, x4 ' 2.00000009. Generally, the number of signifificant decimal digits of

exactness could you expect in x5? Make sense of your response. [4 marks]

8CST.2001.4.9

10 Computer Graphics and Image Processing

(a) Describe a calculation to define a straight boundary utilizing just number math.

You might expect that the line is in the fifirst octant, that the line begins and

closes at number co-ordinates, and that the capacity setpixel(x, y) turns on the

pixel at area (x, y). [8 marks]

(b) Describe Douglas and Pucker's calculation for eliminating superflfluous focuses from

a line chain. [10 marks]

(c) Under what conditions would utilizing Douglas and Pucker be reasonable

calculation?

(a) A combinational rationale circuit takes a 4-bit unsigned paired number at its

inputs named D3 , D2 , D1 and D0 , where D3 is the most signifificant bit. For

decimal info 1, 2, 3, 5, 7, 11 and 13, the result S is to be at rationale 1, and it is

to be at rationale 0 in any case.

1st attempt Prescription drugs are often available in two versions - a name brand and a generic brand. As the price of the name brand falls, the price change Choose one: A. will have no effect on the market demand for the generic brand. 4/15 > B. causes a decrease in the quantity demanded of the generic brand. See Hint C. causes an increase in the quantity demanded of the generic brand. D. causes a decrease in the demand for the generic brand. E. causes an increase in the demand for the generic brand. O SUBMIT