1. (a) Consider the following algorithm: Input: A number k 20 Output: ?? X +0 Y +1 while x k do X +X+1 Y + Y * X return Y i. Give the output of this algorithm in terms of the input. ii. Write a loop invariant for this algorithm.

Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
icon
Related questions
Question

please send answer Q1 for part a ii

please send proper answer

1. (a) Consider the following algorithm:
Input: A number k 20
Output: ??
X +0
Y +1
while x k do
X + x+1
Y +Y * X
return Y
i. Give the output of this algorithm in terms of the input.
ii. Write a loop invariant for this algorithm.
iii. State and use the While-loop invariance theorem to prove that this algorithm
is correct with respect to the output you gave in Part i.
iv. Rewrite the algorithm using a For-loop rather than a While-loop.
(b) Derive the following judgement using natural deduction:
A implies (B and C), B implies D, C implies E- A implies (D andE)
State clearly all the rules that you use in your derivation.
Transcribed Image Text:1. (a) Consider the following algorithm: Input: A number k 20 Output: ?? X +0 Y +1 while x k do X + x+1 Y +Y * X return Y i. Give the output of this algorithm in terms of the input. ii. Write a loop invariant for this algorithm. iii. State and use the While-loop invariance theorem to prove that this algorithm is correct with respect to the output you gave in Part i. iv. Rewrite the algorithm using a For-loop rather than a While-loop. (b) Derive the following judgement using natural deduction: A implies (B and C), B implies D, C implies E- A implies (D andE) State clearly all the rules that you use in your derivation.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY