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In the memory management schemes used in earlier operating systems, it was necessary to modify the addresses of most programs when they were loaded into memory because they were usually not loaded into memory starting at location 0. The OS program loader was assigned this task, which was called 648 PART FIVE THE SOFTWARE COMPONENT program relocation. Why is program relocation unnecessary when virtual storage is used for memory managementWrite Prolog programs that define the following predicates. Your programs should

ensure that backtracking does not produce spurious alternative solutions.

(a) The nth element of a list: nth(X,N,L) instantiates X to the Nth element of

list L. Assume that list elements are numbered increasing from 1. [4 marks]

(b) The last element of a list: last(X,L) instantiates X to the last element of list L.

[4 marks]

(c) Remove an element from a list: remove(X,L,M) instantiates M to a list

containing all the elements of list L except for every occurrence of term X.

[6 marks]

(d) Substitute one element for another: subst(L,X,Y,M) instantiates M to a list

containing all the elements of list L except that every occurrence of term X in

L is replaced by term Y in M.

Write program to print your name on the screen.

Write program to print "Welcome to C++" on the screen

Write to program to calculate the area of a square.

Write program to find sum of all even numbers between 1 to n.

Write program to print all natural numbers from 1 to n.

A majority gate with three inputs signals logic one on its output if two or more of

its inputs are one, and zero otherwise. A minority gate is its complement.

(a) Give the boolean equation for a minority gate as a sum of products.

(b) Sketch the circuit diagram for a minority gate using NAND gates and inverters.

(c) Sketch the transistor-level circuit diagram for an alternative implementation

as a single stage of CMOS logic. [3 marks]

(d) Calculate the number of transistors required for each implementation.

(e) Assuming that a conducting p-channel has a resistance twice that of a similarly

sized n-channel, use logical effort to compare the performance of the two

implementations.

3 Digital Communication II

(a) The Transmission Control Protocol (TCP) employs a transmit window

and cumulative acknowledgement and timeout system, as well as sequence

numbering of packets, to achieve reliable delivery of data.

(i) Outline the procedure for round-trip time estimation and the calculation

of the retransmission timer.

(ii) Explain the function of buffering at the sender and receiver.

(iii) How do fast retransmit and fast recovery improve performance after

packet loss?

(b) In a wireless network, delay to access the channel due to scheduling of the

media access control protocol, and random packet loss due to interference,

may be non-negligible.

(i) Explain how this can interfere with the round-trip time estimation process

above.

(ii) Explain how this can interfere with the congestion control scheme that

TCP employs.

Information retrieval systems vary in the expressivity of the query languages they

employ. For instance, some systems support proximity search: if two query terms

are connected by the "Next" operator, then only those documents are retrieved

where the query terms appear close together (i.e., within a certain number of words

of each other).

(a) List and briefly describe other ways in which the syntax and the interpretation

of query languages may vary.

(b) Describe with an example how the "Next" operator described above is

implemented efficiently in modern information retrieval systems. Your answer

should include a description of the data structure(s) necessary to support it.

(c) A search engine supports error correction in the following way: If an error is

suspected in a query term, the system provides a link labelled "Did you mean

X?", where X is the corrected term, in addition to its normal results. The

link leads to a list of retrieved documents, corresponding to a variant of the

original query, with X replacing the misspelled term.

(i) Explain why it is non-trivial to implement this feature efficiently.

(ii) Discuss methods for implementing this feature in a realistic setting.

(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]

In the memory management schemes used in earlier operating systems, it was necessary to modify the addresses of most programs when they were loaded into memory because they were usually not loaded into memory starting at location 0. The OS program loader was assigned this task, which was called 648 PART FIVE THE SOFTWARE COMPONENT program relocation. Why is program relocation unnecessary when virtual storage is used for memory managementWrite Prolog programs that define the following predicates. Your programs should

ensure that backtracking does not produce spurious alternative solutions.

(a) The nth element of a list: nth(X,N,L) instantiates X to the Nth element of

list L. Assume that list elements are numbered increasing from 1. [4 marks]

(b) The last element of a list: last(X,L) instantiates X to the last element of list L.

[4 marks]

(c) Remove an element from a list: remove(X,L,M) instantiates M to a list

containing all the elements of list L except for every occurrence of term X.

[6 marks]

(d) Substitute one element for another: subst(L,X,Y,M) instantiates M to a list

containing all the elements of list L except that every occurrence of term X in

L is replaced by term Y in M.

Write program to print your name on the screen.

Write program to print "Welcome to C++" on the screen

Write to program to calculate the area of a square.

Write program to find sum of all even numbers between 1 to n.

Write program to print all natural numbers from 1 to n.

A majority gate with three inputs signals logic one on its output if two or more of

its inputs are one, and zero otherwise. A minority gate is its complement.

(a) Give the boolean equation for a minority gate as a sum of products.

(b) Sketch the circuit diagram for a minority gate using NAND gates and inverters.

(c) Sketch the transistor-level circuit diagram for an alternative implementation

as a single stage of CMOS logic. [3 marks]

(d) Calculate the number of transistors required for each implementation.

(e) Assuming that a conducting p-channel has a resistance twice that of a similarly

sized n-channel, use logical effort to compare the performance of the two

implementations.

3 Digital Communication II

(a) The Transmission Control Protocol (TCP) employs a transmit window

and cumulative acknowledgement and timeout system, as well as sequence

numbering of packets, to achieve reliable delivery of data.

(i) Outline the procedure for round-trip time estimation and the calculation

of the retransmission timer.

(ii) Explain the function of buffering at the sender and receiver.

(iii) How do fast retransmit and fast recovery improve performance after

packet loss?

(b) In a wireless network, delay to access the channel due to scheduling of the

media access control protocol, and random packet loss due to interference,

may be non-negligible.

(i) Explain how this can interfere with the round-trip time estimation process

above.

(ii) Explain how this can interfere with the congestion control scheme that

TCP employs.

Information retrieval systems vary in the expressivity of the query languages they

employ. For instance, some systems support proximity search: if two query terms

are connected by the "Next" operator, then only those documents are retrieved

where the query terms appear close together (i.e., within a certain number of words

of each other).

(a) List and briefly describe other ways in which the syntax and the interpretation

of query languages may vary.

(b) Describe with an example how the "Next" operator described above is

implemented efficiently in modern information retrieval systems. Your answer

should include a description of the data structure(s) necessary to support it.

(c) A search engine supports error correction in the following way: If an error is

suspected in a query term, the system provides a link labelled "Did you mean

X?", where X is the corrected term, in addition to its normal results. The

link leads to a list of retrieved documents, corresponding to a variant of the

original query, with X replacing the misspelled term.

(i) Explain why it is non-trivial to implement this feature efficiently.

(ii) Discuss methods for implementing this feature in a realistic setting.

(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]

Transcribed Image Text:

Enumerable and Recursive Sets 1. Are the following sets recursive? Are they recursively enumerable? Justify your conjectures. a) {x|x is an even integer } b) {i | M; halts for all inputs } c) {i | M; halts only for prime integers } d) {i | M; is not a Turing machine } 2. Prove that if the set A is not recursively enumerable and can be reduced to the set B, then B cannot be recursively enumerable. Unsolvability Problems 3. Show that the following sets are not recursively enumerable. a) {i | W =} b) {i | W = all integers } 4. Show that if P(x, y) is a recursive predicate then the following is r.e. { x | P(x, y) is true for some y } 6 5. A complete set is a recursively enumerable set to which every recursively enumerable set can be reduced. Show that K is a complete set. 6. Prove that every index set which is recursively enumerable is a complete set. 7. Let f(x) be a recursive function. Is its range recursive? r.e.? 8. Is the image of a partial recursive function recursive? r.e.? 9. Prove that a set is recursive if and only if it is finite or can be enumerated in strictly increasing order. Enumerable and Recursive Sets 1. Are the following sets recursive? Are they recursively enumerable? Justify your conjectures. a) {x|x is an even integer } b) {i | M; halts for all inputs } c) {i | M; halts only for prime integers } d) {i | M; is not a Turing machine } 2. Prove that if the set A is not recursively enumerable and can be reduced to the set B, then B cannot be recursively enumerable. Unsolvability Problems 3. Show that the following sets are not recursively enumerable. a) {i | W =} b) {i | W = all integers } 4. Show that if P(x, y) is a recursive predicate then the following is r.e. { x | P(x, y) is true for some y } 6 5. A complete set is a recursively enumerable set to which every recursively enumerable set can be reduced. Show that K is a complete set. 6. Prove that every index set which is recursively enumerable is a complete set. 7. Let f(x) be a recursive function. Is its range recursive? r.e.? 8. Is the image of a partial recursive function recursive? r.e.? 9. Prove that a set is recursive if and only if it is finite or can be enumerated in strictly increasing order.