Question

1. Compute the weakest precondition for the following sequence of statements, given the stated post condition.

Hint: Start by deciding what variable or variables should be mentioned in the precondition. Recall the rule for sequences: the precondition for a statement in a sequence is equal to the post-condition for the statement that precedes it. Note: Your answer will involve a relationship between a and b.

{??}

x = 4 * (3 * y – x);

y = 2 * x – 2;

{y > 10}

Answer 1

Consider y > 10

Substitute y = 2 * x – 2 in the above.

2 * x – 2 > 10

2 * x > 10+2

2 * x > 12

x > 6

Substitute x = 4 * (3 * y – x) in the above.

4 * (3 * y – x) > 6

3 * y – x > 6/4

3 * y – x > 1.5

3 * y > 1.5 + x

y > (1.5 + x)/3

Therefore the weakest precondition is y > (1.5 + x)/3.