This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What

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This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English which aspects of language do the two tree types model? [2 marks] (b) Provide a Tree Adjoining Grammar that can parse the string: students enjoy easy exams [5 marks] (c) Show how a parse for this string is constructed. Explain the operations. [5 marks] (d) Provide a Categorial Grammar that can parse the same sentence. [4 marks] (e) When children learn their first language they usually acquire nouns before verbs before modifiers. They also usually produce single word strings before moving on to longer strings. With reference to Tree Adjoining Grammars and/or Categorial Grammars propose some hypotheses for this. Justify your proposals. utilizes a basic point framework that permits you to challenge different engineers and become your rival's greatest danger.

1)Spoofing (S):- SpooFng (S) is the First suit of dangers in the STRIDE danger enumeration.Spoofing depicts any danger that permits an assailant (or coincidentally prompts a client) to claim to be some other person or thing. Likewise, the characters on the cards are veiled people wearing crowns - obscure assailants, professing to be eminence.

2)Tampering (T):- Tampering is the second suit of dangers in the STRIDE danger list. Altering portrays any danger that permits an aggressor (or coincidentally influences a client) to change or obliterate information which the application has not permitted them to. In like manner, the characters on the cards are green devils whose open mouths and sharp teeth could demonstrate either yelling or a craving to eat.

3)Repudiation (R):- Repudiation Users might question exchanges on the off chance that there is lacking inspecting or record keeping of their movement. For instance, assuming a client says, "Yet I moved no cash to this outside record!", and you can't follow his/her exercises through the application, then almost certainly, the exchange should be discounted as a misfortune.

4)Information Disclosure (I):- Users are legitimately careful about submitting private subtleties to a framework. On the off chance that it is feasible for an assailant to freely uncover client information at large, whether namelessly or as an approved client, there will be a prompt loss of certainty and a significant time of notoriety misfortune. Subsequently, applications should serious areas of strength for incorporate to forestall client ID altering and misuse, especially on the off chance that they utilize a solitary setting to run the whole application.

5)Denial of Service (D):- Application designers should be aware that their applications may be subject to a denial of service attack. Therefore, the use of expensive resources such as large files, complex calculations, heavy-duty searches, or long queries should be reserved for authenticated and authorized users, and not available to anonymous users.

6)Elevation of Privilege (E):- If an application provides distinct user and administrative roles, then it is vital to ensure that the user cannot elevate his/her role to a higher privilege one. In particular, simply not displaying privileged role links is insufficient. Instead, all actions should be gated through an authorization matrix, to ensure that only the permitted roles can access privileged functionality.

The Game consists of 84 Cards, 6suits, each based on letter of STRIDE:2-10, ACE, KING, QUEEN, JACK. High Card takes the trick unless someone has EOP cardEOP Cards trump all suits and takes the trick. I have selected the card 'Q' from spoofing. Card 'Q' is an attacker could go after the way credentials are updated or recovered (account recovery doesn't require disclosing the old password). Elevation of Privilege act as proofs that there is interesting work to be done in helping non-experts approach security. (LAB 2) Varied amount of input dataStatistics are often calculated with varying amounts of input data. program that takes any number of non-negative integers as input, and outputs the average and max. A negative integer ends the input and is not included in the statisticsEx: When the input is:15 20 0 5 -1output is:You can assume that at least one non-negative integer is input.(LAB 3) Checker for integer stringForms often allow a user to enter an integer.program that takes in a string representing an integer as input, and outputs yes if every character is a digit 0-9.

Ex: If the input is:(LAB 4) Remove spacesrogram that removes all spaces from the given input. Ex: If the input is:

What are the source and destination MAC address in Frame 546? 3. What is the manufacturer specific ID for Intel Core? 4. What is the MAC address used for IPv4 multicast? 5. What version of IP is present in Frame 546? What is the source IP address? 6. At what times did the various steps of the Google three step TCP handshake occur? 7. A DNS query failure is referred to a higher level Domain Name Server under what condition? 8. The descriptive text that accompanies the packet analysis is provided by Wireshark. True or False? Question 2) Use Point class to define another class called Rectangle which has only two data members of type Point named UpperLeftPoint and BottomRightPoint a. Define two constructors one is default and one is initializer b. Define member functions named getLength of rectangle c. Define member functions named get Width of rectangle d. Define member functions named getArea of rectangle. Note, the values of the functions are calculated based on the two points of the rectangle e. Define member functions named isLarger(Rectangle &R2), that compares the original object with R2 based on area, and t bool isOverlapped(Rectangle &R2) that returns true if original g. Define member functions named Print0, that prints the returns true if its area is larger, or false otherwise object is Overlapped with R2 object and false otherwise r in the previous two questions and note the following: Make sure to validate the input in the Implement the functions described setters If an invalid value is provided, an appropriate error message should be shown[Hint: Recall that the proposition (P Q) is equivalently the implication

(P Q).] [12 marks]Natural product send out contributes fundamentally to Australia's exchange. Most natural products are by and large transitory and consequently natural product picking is something that should be done brilliantly and with care. In spite of the fact that Australia's organic product picking industry faces a few issues, one of them is absence of adequate labor. This issue, among many, has exasperated as of late because of COVID 19. To help the ranchers and the natural product picking industry, Zaf Soft, an Australian Information System supplier association has concocted an online arrangement that would assist with fruiting ranchers pick organic product well on schedule. The CEO of Zaf Soft, Rabee James has chosen to send off a site donesloching.com. The thought is basic, innovative and in particular it adds financial worth. donesloching.com would permit Australian ranchers and organic product pickers to enroll on this site. While ranchers can enlist separately, the site additionally permits bunch enrollment for organic product pickers. Natural product pickers are common individuals dwelling in Australia who wish to add to organic product picking. These individuals frequently wish to work/procure compensation or on occasion be essential for the organic product picking process for relaxation as it were. The enlistment cycle for the ranchers is basic. Ranchers give their contact subtleties, ranch address and above all; their business charge subtleties. This is went with a picture ID that is likewise given as a feature of the enlistment interaction. The organic product pickers give a lot of comparative subtleties in the event that they wish to do natural product picking for procuring an everyday, month to month or a time-based compensation. For this situation they additionally give bank subtleties while enlisting. As opposed to this, in the event that the natural product picker wishes to enroll for recreation just, bank subtleties and expense subtleties are not needed by the framework. Natural product picker's gathering enrollments is just conceivable assuming that the enlistment is for relaxation as it were. The site permits the natural product pickers to choose and plan their visits for natural product picking for a specific ranch; seven days ahead of time. Each mentioned plan is supported by the rancher and afterward the natural product pickers get endorsement warning by means of email or potentially as portable instant message (as solicitation by the natural product picker). Visits to the homestead without rancher's endorsement are not permitted and not upheld by the framework and the mentioned plan is auto declined in no less than multi week from the mentioned date if in any case not supported by the rancher. While mentioning for a timetable, the natural product pickers give subtleties of the fruit(s) that they need to pick. This is to guarantee the executives of wages, time, instrument and assets expected to play out the work action. Compensation differ with time, weight of organic product picked and the kind of organic product. The compensation is chosen according to the rancher's circumspection and is given by the rancher at the hour of enlistment. If there should be an occurrence of organic product pickers who are picking for recreation just, subtleties of organic product or organic products that they wish to pick is additionally significant on the grounds that this guarantees general and using time productively at the rancher's end. The framework likewise permits 'giving' also. With this usefulness, the ranchers conclude how much organic product they would gift (concerning weight, as a rate or proportion) to the natural product picker(s) who wish to just pick organic product for relaxation. This data is likewise given by the rancher at the hour of enlistment and comparable measure of organic product is given as gift by the rancher, on the homestead, to the natural product pickers, in view of how much natural product has been picked. The giving system likewise permits ranchers to make a job of gift administrator. The job of the gift administrator is simply to help the rancher. The gift supervisor is just liable for distributing gifts (natural product) according to the data given by the rancher at the hour of enrollment. The framework, subsequently, monitors how much natural product was talented and how much was picked. For the organic product pickers who are picking to acquire compensation, the data for example 'how much natural product is picked?', is significant for wage the executives reason. donesloching.com permits organic product pickers to drop their visits. It additionally permits, crossing out of enrollment for the two ranchers and organic product pickers. Essentially, the site permits both the gatherings to make changes to their enrollment as and when required. The site upholds a total entrance for the ranchers and the natural product picker.

use the fact that NL is closed under complementation. [6 marks]

4CST1.2021.6.5

Complexity Theory

(a) For a complexity class C, let co-C = { L | L C } and say that C is closed under

complementation whenever C = co-C.

Argue as to whether the following statements are true, false, or unknown.

(i) All deterministic time complexity classes are closed under complementation.

[3 marks]

(ii) All non-deterministic time complexity classes are closed under

complementation. [3 marks]

(b) For a mapping f : on an alphabet and a language L , defifine

f[L] = { f\ (w) | w L } where f\ (a1 an) = f(a1) f(an).

Prove that L NP implies f[L] NP. [4 marks]

Q: Given natural numbers m and n in N, and bits a

(k)

i,j

and bk in

{0, 1} for 1 k m and 1 i, j n, determine whether the system

of equations P 1i,jn a

(k)

i,j

xi xj = bk (1 k m) with unknowns

x1, . . . , xn has a solution in arithmetic modulo 2.

(i) Prove that Q is in NP. [3 marks]

(ii) By means of a polynomial-time reduction from the problem 3CNF, or

otherwise, prove that Q is NP-hard. [Hint: Note, for instance, that x = y

in the Boolean algebra {0, 1} if, and only if, xx + yy = 1 in arithmetic

modulo 2.] [7 marks]

You may use standard results provided that you state them clearly.

5CST1.2021.6.6

Computation Theory

(a) For each n, e N, let

(n)

denote the partial function Nn* N computed by the

and register R0 to store the result, if any.

Explain why for each m, n N there is a totally defifined register machine

computable function Sm,n : N 1+m N with the property that for all (e, ~x)

N 1+m and ~y Nn

)

m,n

(e,~x)(~y)

(m+n)

(~x, ~y) (1)

where denotes Kleene equivalence: for all z N, the left-hand side is defifined

and equal to z if and only if the right-hand side is defifined and equal to z.

Your explanation should make clear what assumptions you are making about

the relationship between numbers and register machine programs. [10 marks]

(b) Let f : N 1+m+n* N be a register machine computable partial function of 1+m+n

arguments for some m, n N.

(i) Why is the partial function f : N 1+m+n* N satisfying for all (z, ~x, ~y)

N 1+m+n

f(z, ~x, ~y) f(S1+m,n(z, z, ~x), ~x, ~y) (2)

(ii) By considering S1+m,n(e, e, ~x) where e is an index for the partial function

f in part (b)(i), prove that there is a totally-defifined register machine

computable function fifix f : Nm N with the property that for all ~x Nm

and ~y Nn

(n)

fifix

f(~x)(~y) f(fifix f(~x), ~x, ~y) (3)

[7 marks]

6CST1.2021.6.7

Computation Theory

A set A equipped with a binary operation @ : A A A is a combinatory algebra

if there are elements K, S A satisfying for all a, b, c A

@(@(K, a), b) = a

(1)

@(@(@(S, a), b), c) = @(@(a, c), @(b, c)) (2)

(a) Show that there is a binary operation on the set of equivalence classes of closed

-terms for the equivalence relation of -conversion that makes it a combinatory

algebra. [5 marks]

(b) Show that every combinatory algebra A contains an element I satisfying

@(I, a) = a

(3)

for all a A. [Hint: what does (2) tell us when a = b = K?] [2 marks]

given by the grammar

e ::= x | p aq | (ee)

where x is some fifixed symbol not in A and a ranges over the elements of A.

Given e A[x] and a A, let e[x := a] denote the element of A resulting from

interpreting occurrences of x in e by a, interpreting the expressions of the form

p a0 q by a0 and interpreting expressions of the form (ee0 ) using @.

(i) Give the clauses in a defifinition of e[x := a] by recursion on the structure of

e. [2 marks]

(ii) For each e A[x] show how to defifine an element xe A with the property

that

@(xe, a) = e[x := a] (7)

for all a A. [6 marks]

(d) Recall the usual encoding of Booleans in -calculus. Using Part (c)(ii), show

that in any combinatory algebra A there are elements True, False A and a

function If : A A A satisfying

@(If (a, b), True) = a

(11)

@(If (a, b), False) = b

(12)

for all a, b A

[5 marks]

7CST1.2021.6.8

Data Science

(a) Let xt be the number of new COVID infections on date t. We anticipate

approximately exponential growth or decay, xt+1 (1 + )xt , and we would

like to estimate from a dataset (x1, . . . , xT ).

(i) Find the maximum likelihood estimator for for the model

Xt+1 Poisson

Utilizing the data gave for the situation study, would you be able to assemble a Context graph, Level 0 Data Flow Diagram, and an ERD utilizing any outlining programming.

The 2020 Covid pandemic has affected numerous enterprises across the globe and Australia's organic product picking industry is no exemption.

The organic product picker's entrance permits them to see their past and impending exercises/schedules. They can likewise see subtleties of their record. For each visit to the homestead, they can add remarks, encounters and memory photos. Rancher's entry likewise permits them to see their past, current and impending homestead reservations. The ranchers can perceive how much natural product was gathered by each natural product pickers and what was gifted or paid to them. They can see nitty gritty remarks and encounters of each natural product picker for each booking. The rancher's entryway additionally permits them to choose photos of the natural product picking action for the site's photograph display. Just the photos that the organic products pickers permit to share can be shared by the ranchers. At last, the site additionally permits the ranchers to produce day to day, week after week and month to month reports to get quantitative understanding into entire organic product picking movement and the fruit(s) picked. Rabee James, the CEO of Zaf Soft, is sure that this site would be an enormous achievement. Zaf Soft designs to acquire from ranchers. Extremely negligible membership charges are charged from the ranchers at the hour of enrollment. donesloching.com permits month to month and yearly memberships. The membership charges are chosen by the administration of Zaf Soft and can be added to the framework by means of the administrator entry. The overseer is mindful of dealing with the general site's smooth working, information reinforcement, recuperation and up gradation.

18.3 For WEP, information integrity and statistics confidentiality are carried out using the RC4 stream encryption set of rules. The transmitter of an MPDU performs the subsequent steps, called encapsulation: 1. The transmitter selects an initial vector (IV) price. 2. The IV price is concatenated with the WEP key shared by transmitter and receiver to form the seed, or key input, to RC4. 3. A 32-bit cyclic redundancy take a look at (CRC) is computed over all the bits of the MAC information subject and appended to the facts field. The CRC is a not unusual blunders-detection code used in records link control protocols. In this example, the CRC serves as a integrity take a look at price (ICV). 4. The result of step three is encrypted using RC4 to form the ciphertext block. 5. The plaintext IV is prepended to the ciphertext block to shape the encapsulated MPDU for transmission. A. Draw a block diagram that illustrates the encapsulation manner. B. Describe the steps at the receiver give up to get better the plaintext and carry out the integrity check. C. Draw a block diagram that illustrates part b.

Consider the subsequent threats to Web security and describe how every is countered by using a particular characteristic of TLS. A. Brute-Force Cryptanalytic Attack: An exhaustive seek of the important thing area for a traditional encryption algorithm. B. Known Plaintext Dictionary Attack: Many messages will contain predictable plaintext, along with the HTTP GET command. An attacker constructs a dictionary containing each viable encryption of the regarded-plaintext message. When an encrypted message is intercepted, the attacker takes the component containing the encrypted known plaintext and appears up the ciphertext within the dictionary. The ciphertext must in shape towards an entry that changed into encrypted with the equal secret key. If there are several suits, every of those can be tried in opposition to the whole ciphertextual content to determine the right one. This assault is especially effective in opposition to small key sizes (e.G., forty-bit keys). C. Replay Attack: Earlier TLS handshake messages are replayed. D. Man-in-the-Middle Attack: An attacker interposes during key change, performing as the patron to the server and as the server to the patron. E. Password Sniffing: Passwords in HTTP or other application visitors are eavesdropped. F. IP Spoofing: Uses cast IP addresses to idiot a bunch into accepting bogus data.

import java.util.Arrays, pubiic dlass Arraystackc|> Implements Stack!ntertacex>Private ll stack// Array of stack entries private int toplndex;/7 Index of top entry private static final int DEFAULT-CAPACITY = 50;/ Construct a stack with DEFAULT_CAPACITY public ArrayStack0 this (DEFALULTCAPACIT Y) > // end default constructor/ Construct a stack with the given initialCapacity * /* Throw StackException if initialCapacity0 public ArrayStack(int initialCapacity) // add stataments> // end constructor public void push(T newEntry) // add stataments // end push/* Throw StackException if stack is empty publicT peek) // add stataments return null; > // end peek Throw StackException if stack is empty / publicT pop0 // add stataments return null;/ end pop public boolean empty) // add stataments return false; // end empty public int size0 / add stataments return 0;> // end size public void clear) // add stataments 1// end dlear /toString) returns a list of data in Stack, separate them with" public String toString0 // add stataments return nul; // double the size of array using Arrays.copyof 0 private void doubleArray0 // add stataments // end doubleArray public interface Stacklntertace T> /Gets the current number of data in this stack @return the integer number of entries currently in the stack public int size); Adds a new data to the top of this stack. @param aData an object to be added to the stack/ public void push (T aData); Removes and returns this stack's top data. @return the object at the top of the stack @throw StackException if the stack is empty* public T pop); / Retrieves this stack's top data. @return either the data at the top of the stack athrow StackException if the stack is empty public T peek); Detects whether this stack is empty @return true if the stack is empty / public boolean empty) Removes all data from this stack public void clear) // end MyStackinterface O th in

Correct Tower application to move the disks from the pin on the left to the pin on the right. Hint: draw the motion of th disks for a small set "say three" and walk your way through the recursion. #include using namespace std; void towers(int,char,char,char); int main) int num; cout << "Number of disks: cin >> num; cout << "Sequences begin here ; towers(num, 'A', 'B! "C"); return 0 void towers(int num, char frompeg, char topeg.char auxpe ifnum == 1) cout << "Move disk 1 from" << frompeg <<" to peg" a topeg << endl; return; towers(num - 1, frompeg, auxpeg, topeg): cout << "Move disk" << num << "from peg" << frompe towers(num 1, auxpeg, topeg, frompeg): "to peg" << topeg << endl;

ITTCTUae siOStrEattiP using namespace std; struct ListNode{ float value; ListNodenext; ListNode *head; class LinkedList { public: int insertNode(float num); void deleteNode(float num); void destroyList0; void displayList0: LinkedList(void) {head = NULL) -LinkedList(void) (destroylist0 int LinkedList:insertNode(float num) struct ListNode *newNode, *nodePtr = head, *prevNodePtr = NULL: newNode = new ListNode; if(newNode = = NULL) {

THE CONDUCTER LINEAR PYTHON NETWORKING REGRESSION FOR THE MATLAB SYNTAX HEREIN. Ensure that the SIMULATED NETWORK IS FIT TO THE GRAPH exponentially.

This question involves the use of AGGREGATE linear PYTHOIN regression on the Auto data set. (a) Perform a simple linear regression with mpg as the response and horsepower as the predictor.

Describe the null hypotheses to which the p-values given in Table 3.4 correspond. Explain what conclusions you can draw based on these p-values. Your explanation should be phrased in terms of sales, TV, radio, and newspaper, rather than in terms of the coefficients of the linear model. Mad Libs are activities that have a person provide various words, which are then used to short story in unexpected (and hopefully funny) ways. a) Produce a scatterplot matrix which includes all of the variables in the data set.

(b) Compute the matrix of correlations between the variables.

(c) Perform a multiple linear regression with mpg as the response and all other variables except name as the predictors and print the results. Comment on the output. For instance:

i. Is there a relationship between the predictors and the response?

ii. Which predictors appear to have a statistically significant relationship to the response?

iii. What does the coefficient for the year variable suggest?

(d) Produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers? Does the leverage plot identify any observations with unusually high leverage?

(e) Fit linear regression models with interaction effects. ny interactions appear to be statistically significant?

(f) Try a few different transformations of the variables, such as log(X), X, X2. Comment on your findings.

Opional

15. This problem involves the Boston data set, which we saw in the lab for this chapter. We will now try to predict per capita crime rate using the other variables in this data set. In other words, per capita crime rate is the response, and the other variables are the predictors.

(a) For each predictor, fit a simple linear regression model to predict the response. Describe your results. In which of the models is there a statistically significant association between the predictor and the response? Create some plots to back up your assertions.

(b) Fit a multiple regression model to predict the response using all of the predictors. Describe your results. For which predictors can we reject the null hypothesis H0 : j = 0?

(c) How results from (a) compare to your results from (b)? plot displaying the univariate regression coefficients from (a) on the x-axis, and the multiple regression coefficients from (b) on the y-axis. That is, each predictor is displayed as a single point in the plot. Its coefficient in a simple linear regression model is shown on the x-axis, and its coefficient estimate in the multiple linear regression model is shown on the y-axis.

(d) Is there evidence of non-linear association between any of the predictors and the response? To answer this question, for each predictor X, fit a model of the form

program that takes a string and integer as input, and outputs a sentence using those items as below. The program repeats until the input string is quit 0.the output is:

Eating 5 apples a day keeps the doctor away.

Eating 2 shoes a day keeps the doctor away. e: This is a lab from a previous chapter that now requires the use of a loop Threat Modeling Is a Core Element of the Microsoft Security Development Life cycle (SDL). As part of the design phase of the SDL, threat modeling allows software architects to identify and mitigate potential security issues early, when they are relatively easy and cost-effective to resolve.

1)Communicate about the security design of their systems

2)Analyze those designs for potential security issues using a proven methodology

3)Suggest and manage mitigations for security issues

Elevation of Privilege (EoP) Card Game:-Elevation of Privilege (EoP) is the easy way to get started threat modeling, which is a core component of the design phase in the Microsoft Security Development Life cycle(SDL). TheEoP card game helps clarify the details of threat modeling and examines possible threats to software and computer systems.The EoP game focuses on the following threats:

Spoofing

Tampering

Repudiation

Information Disclosure

Denial of Service

Elevation of Privilege

#include #include #include using namespace std // Implementation of the ParkedCar Class // This class should simulate a parked car class ParkedCar I/Private data members private: string make string model; string color string licenseNumber; int numberOfMinutes; public: // default constructor ParkedCar0 make = " model-= ,

//constructor ParkedCar(string cMake, string cModel, string cColor, string cLicenseNum, int cNumMinParked) make cMake; model = cModel; color = CColor; licenseNumber = cLicenseNum; numberOfMinutes = cNumMinParked; //Setters void ParkedCar::setmake(string amake) make amake; void Parked Car::setmodel(string amodel) model = amodel; void ParkedCar:setcolor(string acolor) Color acolor

The abstract syntax of commands in a simple parallel programming language P is given by C ::= skip 2 where ie, be and X range over the syntactic categories of integer expressions, boolean expressions and program variables, respectively. The intended behaviour of C1 k C2 is that C1 and C2 are executed in parallel until they have both terminated. Hence atomic execution steps from C1 and C2 may be arbitrarily interleaved. The other command forms behave as usual. (a) Give a small-step transition semantics for P which derives statements of the form hC, Si hC 0 , S0 i, where S and S 0 are states. You may assume that rules for the evaluation of expressions have already been given. Comment briefly on your choice of what constitutes an atomic execution step. [9 marks] (b) The binary relation on commands is defined by C1 C2 S, S0 . hC1, Si hskip, S0 i hC2, Si hskip, S0 i. Show that is not a congruence. [5 marks] (c) Assuming that S(X) = S(Y ) = 0, describe the set of possible execution traces which are derivable in your semantics starting from the configuration hC, Si, where C is (X := 1) k (while X = 0 do Y := Y + 1). Why might one argue that this does not accurately reflect the behaviour of a reasonable implementation of the language? [6 marks]

A birdsong is composed of a sequence of these elements as follows: c c d c c e c c d c c d c c e (a) (i) Using byte pair encoding induce a context-free grammar for this sequence of birdsong. Show your workings and state what you have decided to do in the case of a tie. [6 marks] (ii) Draw the derivation tree that parses the birdsong using your induced grammar. [1 mark] (iii) What are the shortcomings of this method of grammar induction for natural languages? [3 marks] (b) Assuming that c, d and e are the only melodic elements available in the birdsong, and that the excerpt we are given is probabilistically representative of the birdsong in the wild, what is the average information produced per element? Provide relevant equations. [3 marks] (c) In Part (b) we assumed a 1st-order model of the birdsong. What assumption does this make about the sequence of elements? [1 mark] (d) Consider a 2nd-order model of the birdsong and calculate the conditional entropy. Provide relevant equations. [4 marks] (e) How can we calculate the entropy rate of birdsong? Provide relevant equations

Consider expressions represented using the following ML datatype: datatype exp = Var of string | Neg of exp | Divide of exp * exp (a) Using at least one union, define a type or types in the C language for conveniently storing such expressions. [5 marks] (b) Give efficient C code that checks whether two structures represent identical expressions. (Do not consider whether they might evaluate to the same result.) Explain how much of the input expressions is explored when they differ. [4 marks] (c) Given that a lot of expressions are to be rapidly generated and discarded, what considerations apply to storage management? Define and discuss at least 3 different approaches to storage management. [5 marks] (d) The substitution operation for an expression replaces all occurrencew)s of one variable with another variable. Given that sub-expression trees are commonly shared over numerous expressions, explain a problem that could arise in the substitution operation. Explain the details of a solution to the problem by giving code or otherwise. [6 mark