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4. Potential Function Consider the following function, which takes in non-negative integers a and b that are powers of two. 1: function ALG(a,b) if a = 1 or b =1 or a = b then return 0 if a > b then return ALG(a/2, 2b) if b > a then return ALG(2a, b/2) 2: 3: 4: Which of the following functions can be used as a potential function to prove that the algo- rithm ALG halts on all valid inputs a, b? a +b a * b a/b |6 – a| None of these functions works as a potential function for ALG.

4. Potential Function Consider the following function, which takes in non-negative integers a and b that are powers of two. 1: function ALG(a,b) if a = 1 or b =1 or a = b then return 0 if a > b then return ALG(a/2, 2b) if b > a then return ALG(2a, b/2) 2: 3: 4: Which of the following functions can be used as a potential function to prove that the algo- rithm ALG halts on all valid inputs a, b? a +b a * b a/b |6 – a| None of these functions works as a potential function for ALG.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. Potential Function Consider the following function, which takes in non-negative integers a and b that are powers of two. 1: function ALG(a,b) 2: if a = 1 or b = 1 or a = b then return 0 3: if a > b then return ALG(a/2, 2b) 4: if b > a then return ALG(2a, b/2) Which of the following functions can be used as a potential function to prove that the algo- rithm ALG halts on all valid inputs a, b? a +b a * b a/b |6 – a| None of these functions works as a potential function for ALG.
Transcribed Image Text:4. Potential Function Consider the following function, which takes in non-negative integers a and b that are powers of two. 1: function ALG(a,b) 2: if a = 1 or b = 1 or a = b then return 0 3: if a > b then return ALG(a/2, 2b) 4: if b > a then return ALG(2a, b/2) Which of the following functions can be used as a potential function to prove that the algo- rithm ALG halts on all valid inputs a, b? a +b a * b a/b |6 – a| None of these functions works as a potential function for ALG.
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