if x < 15:
x = x+1
else:
x = 0
the post condition is: Q = {0 <= x <= 15}
is the correct pre condition P1 = {-1 <= x} or P2 = {0 <= x <= 15}
And how can I calculate it?
Hoare Logic, calculate pre condition
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Both are valid preconditions for the code fragment and postcondition, so you want to choose the weaker one, which in this case is P1. (P2 specifies a narrower range of values for x, all of which are present in the range specified by P1.)