Given the following code fragment, where x is a number.
{ y >= 0 }
z = 0
n = y
while (n > 0) begin
z = z + x
n = n – 1
end
What does it compute? Prove it, showing how you derive the loop invariant.
How can I do that please?
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Yu Hao
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user2977595
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I guess that it computes the sum of a number, like the factoriel but with the sum no? For the part of the loop invariant I have no idea – user2977595 Mar 01 '14 at 09:34
2 Answers
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This example is known like most correct program, because it is proved in every software verification course. Here is listing of the program with invariants on every step:
{ y >= 0 }
z = 0 // invariant: z = 0
n = y // invariant: n = y and z = 0
while (n > 0) begin // loop invariant: y * x - n * x = z
z = z + x
n = n – 1
end
// Final invariant: n = 0 and y * x = z
All theoretical details for this example are provided in my paper page 118.
mathfac
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For given X and Y it computes X * Y.
at the beginning, value of the Z is zero, and the N = Y (loop's variable which will countdown in our loop).
the loop executes Y times and in every time that it executes, it accumulates the X to the Z.
finally, when the N reached to 0 the loop will terminate, then the value of Z should be X * Y.
Ali Adlavaran
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Thanks but do you know how to show it by deriving the loop invariant please? – user2977595 Mar 01 '14 at 13:48