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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.

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)
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...
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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.
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