Question 1

Are all problems in P solvable in a reasonable amount of time? Explain your answer.

Accepted Answer

No. Simply because the time complexity of a problem is bounded by a polynomial does not mean that the problem can be solved quickly. If the degree of the polynomial is large, the time required could be enormous-even for small inputs.

Question 2

What is a universal programming language?

Accepted Answer

A universal programming language is a programming language with which a solution to any solvable problem can be expressed.

Question 3

Why is a public key encryption system based on the RSA algorithm secure?

Accepted Answer

It is secure because no one knows a fast way to find the prime factors of the public key n.

Question 4

Is a problem in O(n3) more complex than a problem in O(n2)? Explain your answer.

Accepted Answer

Not necessarily. To say that p

Question 5

Write a sequence of statements in the Bare Bones language that is equivalent to the statement
if X not 0 then S1 else S2
where S1 and S2 are sequences of Bare Bones statements.

Accepted Answer

One soluti

Question 6

Place an X in the blank before each of the following statements that guarantees that a problem is in P.

Accepted Answer

First, thi

Question 7

Which of the following questions has not yet been answered by researchers?

Accepted Answer

A)  Is P contained in NP? 
B)  Is NP contained in P? 
C)  Are all the problems in NP solvable? 
D)  Are all the problems in P solvable? 
A)  Is P contained in NP? 
B)  Is NP contained in P? 
C)  Are all the problems in NP solvable? 
D)  Are all the problems in P solvable?

Question 8

If an RSA public key encryption system were based on the primes p = 3 and q = 7, which of the following pairs of values would be suitable for the encryption and decryption keys e and d?

Accepted Answer

A)  2 and 6 
B)  5 and 29 
C)  4 and 9 
D)  7 and 23 
A)  2 and 6 
B)  5 and 29 
C)  4 and 9 
D)  7 and 23

Question 9

Place a T in the blank before each of the following statements that are true. Leave the other blanks blank.
_____ All Bare Bones programs that do not contain a while statement are self-terminating.
_____ All Bare Bones programs that contain a while statement are not self-terminating.
_____ Some Bare Bones programs are both self-terminating and not self-terminating.
_____ No Bare Bones program is both self-terminating and not self-terminating.

Accepted Answer

The answer of Place a T in the blank before...

Question 10

Identify a problem that does not have an algorithmic solution.
_____________________

Accepted Answer

The most l

Question 11

Which of the following best describes what the following Bare Bones program does? copy X to Z;
Clear X;
Incr X;
While Z not 0 do;
Clear X;
Decr Z;
End;

Accepted Answer

A)  It changes the value of X to 1. 
B)  If the starting value of X is 0, it sets the value of X to 0. Otherwise, it sets the value of X to 1. 
C)  If the starting value of X is 0, it sets the value of X to 1. Otherwise, it sets the value of X to 0. 
D)  It ultimately leaves X the same as it was when the program started. 
A)  It changes the value of X to 1. 
B)  If the starting value of X is 0, it sets the value of X to 0. Otherwise, it sets the value of X to 1. 
C)  If the starting value of X is 0, it sets the value of X to 1. Otherwise, it sets the value of X to 0. 
D)  It ultimately leaves X the same as it was when the program started.

Question 12

Which of the following algorithms represents an optimal solution (in terms of time complexity) for sorting a list?

Accepted Answer

A)  Insertion sort 
B)  Bubble sort 
C)  Selection sort 
D)  Merge sort 
A)  Insertion sort 
B)  Bubble sort 
C)  Selection sort 
D)  Merge sort

Question 13

Place an X in the blank before each of the following statements that contradict the Church-Turing thesis. Leave the other blanks blank.
_____ All functions are computable.
_____ Some functions that are not computable by Turing machines are computable by other
means.
_____ All computable functions are Turing-computable.
_____ Some problems cannot be solved by any Turing machine.

Accepted Answer

The answer of Place an X in the blank before...

Question 14

What is the time complexity of the problem of sorting a list?

Accepted Answer

A)   $ \varTheta$(lg n) 
B)   $ \varTheta$(n) 
C)   $ \varTheta$(n lg n) 
D)   $ \varTheta$(n2) 
A)   $ \varTheta$(lg n) 
B)   $ \varTheta$(n) 
C)   $ \varTheta$(n lg n) 
D)   $ \varTheta$(n2)

Question 15

Which of the following sets of values constitutes a valid RSA public key encryption system?

Accepted Answer

A)  p = 5, q = 11, n = 55, e = 17, d = 13 
B)  p = 5, q = 11, n = 83, e = 17, d = 13 
C)  p = 5, q = 11, n = 83, e = 10, d = 13 
D)  p = 5, q = 11, n = 55, e = 10, d = 13 
A)  p = 5, q = 11, n = 55, e = 17, d = 13 
B)  p = 5, q = 11, n = 83, e = 17, d = 13 
C)  p = 5, q = 11, n = 83, e = 10, d = 13 
D)  p = 5, q = 11, n = 55, e = 10, d = 13

Question 16

Suppose the variables X and Y in the following Bare Bones program have the values 3 and 2, respectively, when execution begins. clear Z;
While X not 0 do;
While Y not 0 do;
Decr Y;
Incr Z;
End;
Incr Z;
Decr X;
End;
What will be the value of Z when the program terminates?

Accepted Answer

A)  0 
B)  1 
C)  5 
D)  6 
A)  0 
B)  1 
C)  5 
D)  6

Question 17

Give an example of a universal programming language.
_____________________

Accepted Answer

The most likely answer is Bare

Question 18

Write a program in Bare Bones that terminates with the variable Z equal to 1 if the variables X and Y start with non-zero values and with Z equal to 0 otherwise.

Accepted Answer

One soluti

Question 19

If a solution with time complexity  $ \varTheta$(n2) is known to exist, then the problem is known to be in which of the following?

Accepted Answer

A)   $ \varTheta$(n2) 
B)  O(n2) 
C)   $ \varTheta$(n3) 
D)   $ \varTheta$(n) 
A)   $ \varTheta$(n2) 
B)  O(n2) 
C)   $ \varTheta$(n3) 
D)   $ \varTheta$(n)

Question 20

What action is performed by the Turing machine described below?

Accepted Answer

A)  It replaces any string of consecutive 1s to the left of an * with 0s. 
B)  It leaves the tape unchanged. 
C)  It places an * at the left end of any string of consecutive 1s appearing to the left of an *. 
D)  It complements the string of 0s and 1s appearing to the left of an *. 
A)  It replaces any string of consecutive 1s to the left of an * with 0s. 
B)  It leaves the tape unchanged. 
C)  It places an * at the left end of any string of consecutive 1s appearing to the left of an *. 
D)  It complements the string of 0s and 1s appearing to the left of an *.

Are all problems in P solvable in a reasonable amount of time? Explain your answer.

What is a universal programming language?

Why is a public key encryption system based on the RSA algorithm secure?

Is a problem in O(n³) more complex than a problem in O(n²)? Explain your answer.

Write a sequence of statements in the Bare Bones language that is equivalent to the statement if X not 0 then S1 else S2 where S1 and S2 are sequences of Bare Bones statements.

Place an X in the blank before each of the following statements that guarantees that a problem is in P.

Which of the following questions has not yet been answered by researchers?

If an RSA public key encryption system were based on the primes p = 3 and q = 7, which of the following pairs of values would be suitable for the encryption and decryption keys e and d?

Identify a problem that does not have an algorithmic solution. _____________________

Which of the following best describes what the following Bare Bones program does? copy X to Z; Clear X; Incr X; While Z not 0 do; Clear X; Decr Z; End;

Which of the following algorithms represents an optimal solution (in terms of time complexity) for sorting a list?

What is the time complexity of the problem of sorting a list?

Which of the following sets of values constitutes a valid RSA public key encryption system?

Suppose the variables X and Y in the following Bare Bones program have the values 3 and 2, respectively, when execution begins. clear Z; While X not 0 do; While Y not 0 do; Decr Y; Incr Z; End; Incr Z; Decr X; End; What will be the value of Z when the program terminates?

Give an example of a universal programming language. _____________________

Write a program in Bare Bones that terminates with the variable Z equal to 1 if the variables X and Y start with non-zero values and with Z equal to 0 otherwise.

If a solution with time complexity $\varTheta$ (n²) is known to exist, then the problem is known to be in which of the following?

What action is performed by the Turing machine described below?

Data Storage

Data Manipulation

Operating Systems

Networking and the Internet

Algorithms

Programming Languages

Software Engineering

Data Abstractions

Database Systems

Computer Graphics

Theory of Computation

Filters

Exam 11: Artificial Intelligence

Are all problems in P solvable in a reasonable amount of time? Explain your answer.

What is a universal programming language?

Why is a public key encryption system based on the RSA algorithm secure?

Is a problem in O(n3) more complex than a problem in O(n2)? Explain your answer.

Write a sequence of statements in the Bare Bones language that is equivalent to the statement if X not 0 then S1 else S2 where S1 and S2 are sequences of Bare Bones statements.

Place an X in the blank before each of the following statements that guarantees that a problem is in P.

Which of the following questions has not yet been answered by researchers?

If an RSA public key encryption system were based on the primes p = 3 and q = 7, which of the following pairs of values would be suitable for the encryption and decryption keys e and d?

Identify a problem that does not have an algorithmic solution. _____________________

Which of the following best describes what the following Bare Bones program does? copy X to Z; Clear X; Incr X; While Z not 0 do; Clear X; Decr Z; End;

Which of the following algorithms represents an optimal solution (in terms of time complexity) for sorting a list?

What is the time complexity of the problem of sorting a list?

Which of the following sets of values constitutes a valid RSA public key encryption system?

Suppose the variables X and Y in the following Bare Bones program have the values 3 and 2, respectively, when execution begins. clear Z; While X not 0 do; While Y not 0 do; Decr Y; Incr Z; End; Incr Z; Decr X; End; What will be the value of Z when the program terminates?

Give an example of a universal programming language. _____________________

Write a program in Bare Bones that terminates with the variable Z equal to 1 if the variables X and Y start with non-zero values and with Z equal to 0 otherwise.

If a solution with time complexity Θ \varThetaΘ (n2) is known to exist, then the problem is known to be in which of the following?

What action is performed by the Turing machine described below?

Data Storage

Data Manipulation

Operating Systems

Networking and the Internet

Algorithms

Programming Languages

Software Engineering

Data Abstractions

Database Systems

Computer Graphics

Theory of Computation

Filters

Is a problem in O(n³) more complex than a problem in O(n²)? Explain your answer.

If a solution with time complexity $\varTheta$ (n²) is known to exist, then the problem is known to be in which of the following?