Write a loop invariant for this algorithm. 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.

Computer Networking: A Top-Down Approach (7th Edition)
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Chapter1: Computer Networks And The Internet
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1. (a) Consider the following algorithm:
Input: A number k 20
OUutput: ??
X +0
Y 1
while x k do
X +x+1
Y EY * 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 EH 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 OUutput: ?? X +0 Y 1 while x k do X +x+1 Y EY * 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 EH A implies (D andE) State clearly all the rules that you use in your derivation.
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