definitions for all operations you use. [5 marks] (b) State precisely what it means for a function f : N k ? N to be ?-definable. [5 marks] (c) For each of the following functions, show (using the definitions you gave) that it is primitive recursive and ?-definable. (i) The function square : N ? N given by square(x) = x 2 . [4 marks] (ii) The function fact : N ? N given by fact(x) = x!. [4 marks] (d) Give a definition of a function that is ?-definable but not primitive recursive. [2 marks] 4 CST.2011.6.5 5 Logic and Proof (a) Recently, automated theorem provers based on the saturation algorithm have become very powerful tools. (i) Exhibit a proof by resolution of the following formula in first-order logic. Include the conversion into a set of clauses and provide brief justification for each step of the proof. ?x(P(x) ? Q(x)) ? (?yP(y) ? ?zQ(z))

(a) Name five different types of intellectual property.

(b) Distinguish between "Deep linking" and "Direct linking". Can a search engine

deep link without infringing the copyright of the original site?

(c) Why is the use of thumbnails of pictures by a search engine fair use?

(d) Why are there likely to be only a few dominant search engines?

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?

(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.

(a) (i) Briefly describe the purpose of broadband fixed wireless access (FWA)

and give typical situations where it could be deployed.

(ii) What advantages does radio offer over traditional wired access?

(b) Explain how intersymbol interference (ISI) arises in a wireless communication

system and its effect on system performance.

(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?

(iii) Highlight problems that arise with the use of OFDM. In what situation

is OFDM preferred over the use of equalisation?

(a) Describe, with examples, the function of a naming service for a largescale distributed system. Include definitions for "name space" and "naming

domain".

(b) Discuss consistency versus availability for naming data in large-scale systems.

(c) How can any distributed naming service be engineered so that invocations on

behalf of users can be resolved efficiently in the presence of failures and heavy

load?

(d) Contrast the assumptions under which DNS was designed originally for the

Internet, with the properties of dynamically formed groups of mobile hosts

using wireless communication (MANETS). How might DNS-like services be

provided for MANETS?

5 Advanced Systems Topics

Modern peer-to-peer (P2P) systems are typically described as structured or

unstructured.

(a) Compare and contrast these two approaches. Include a discussion of the

general topology, membership management and query mechanisms. Use

examples to support your answer.

(b) Which approach is more resilient to churn? Justify your answer.

(c) One early criticism of P2P systems was that they did not consider network

latencies. Describe how one can add proximity awareness to:

(i) unstructured P2P systems

(ii) structured P2P systems.

(d) Swarming P2P systems like BitTorrent are designed for efficient (and incentive

compatible) download of large files. However, it is typically not possible to use

the file until it has downloaded in its entirety. Sketch the design of a swarming

P2P system which supports streaming video - that is, allows playback of video

to overlap the ongoing download of the remainder of the stream. Comment

on how efficient (in terms of network resources) your system would be in

comparison with a system like BitTorrent

Some banks issue their Automatic Teller Machine (ATM) card customers with

a randomly selected personal indentification number (PIN). Others issue their

customers with an initial PIN only, and let the customers choose their own PIN the

first time they use the card in an ATM. Describe the advantages and disadvantages

of these approaches. [5 marks]

Again, some banks compute the customer PIN by encrypting the account number

using DES and a key known only to their central systems and ATMs, taking the first

four hex digits of the result, replacing the digits A, . . . , F with 0, . . . , 5 respectively,

and finally, if the first digit of the result is 0, replacing it with a 1. What is the

probability that a criminal can get the PIN right given three guesses? [5 marks]

Yet other banks have used DES, and a key known only to their central systems and

ATMs, to encrypt the PIN (whether randomly generated or customer selected); they

then write the result on the magnetic strip on the customer's card, so that the ATM

can verify it without reference to the central system. Describe the disadvantages

of this arrangement. [5 marks]

In order to prevent attacks based on manipulating magnetic strips, banks in some

countries have moved to using smart cards. What effect would you expect such a

move to have on the incidence of card-based fraud? [5 marks]

5 [TURN OVER

CST.98.12.6

7 Compiler Construction

Explain how a parse-tree representation of a program may be converted into a

stack-based intermediate language giving sketches of code to translate expressions,

assignments and the if-then-else command; you should also explain how

occurrences of a variable in an expression or assignment are translated.

The program may be assumed to conform to the following syntax:

E -> n | x | E + E | f(E,E)

D -> let f(x,x) = {Dseq; Cseq; E} | let x = E

C -> x := E; | if E then C else C

Cseq -> C | C Cseq

Dseq -> D | D Dseq

with start symbol Dseq. Here n corresponds to integer constants, x corresponds to

identifiers used as variable names and f corresponds to identifiers used as function

names (you may assume these are disjoint)

1.(TCO 1) The.javaextension on a file means that the file(Points: 6) contains Java source code. contains HTML. is produced by the Java compiler (javac). contains a machine specific executable image. 2.(TCO 1) Every Java application is required to have(Points: 6) at least one public static method called main. at least one data member. a String variable which holds the name of the application. a content pane and several GUI components. 3.(TCO 1) Which is a correct way to invoke the static method sqrt of the Math class? (Points: 6) sqrt(900); math.sqrt(900); Math.sqrt(900); Math math= new Math(); math.sqrt( 900); 4.(TCO 1) Which line below creates a String object that displays the value of current to 3 decimal digit accuracy, given voltage and resistance variables which are of type double? (Points: 6) String res=