1 transparent par page - Montefiore

Exponentiation
1 x = a ; y = 1 ; z = b
2 while z = 0
3 r = remainder(z, 2)
4 z = quotient(z, 2)
5 if r = 1
6 y = xy
7 x = x 2
Machine d’état :
◮ Q = R × R × N
◮ Q0 = {(a, 1, b)}
◮ δ =
Pre((x, y, z)) = “x ∈ R, z ∈ Z”
Post((x, y, z)) = “y = a b ”
(remainder(q, r) = q mod r et quotient(q, r) = ⌊ q
r ⌋)
(x, y, z) →
(x 2 , y, quotient(z, 2)) si z = 0 et z pair
(x 2 , xy, quotient(z, 2)) si z = 0 et z impair
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