Compute the weakest precondition for each of the following assignment statements and postconditions. x = 2 * y -5; y = x + 2; {y < 2}
Compute the weakest precondition for each of the following assignment statements and postconditions.
x = 2 * y -5;
y = x + 2;
{y < 2}
We can compute the weakest precondition for a given assignment statement and postcondition by working backwards using the rules of Hoare logic.
For the first assignment statement, we want to find a precondition P such that if P is true before the statement executes, then the postcondition {y < 2} is true after the statement executes. Using algebra, we can rewrite the assignment statement as y = (x + 5) / 2, so we have:
{y < 2} => {(x + 5) / 2 < 2}
=> {x + 5 < 4}
=> {x < -1}
Therefore, the weakest precondition for the assignment statement x = 2 * y - 5 and the postcondition {y < 2} is x < -1.
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