Question

Compute the weakest precondition for each of the following assignment statements and postconditions:

a = 2 * (b - 1) - 1 {a > 0}
b = (c 10) / 3 {b > 6}
a. b > 1, c > 16
b. b > 1, c < 16
c. b < 1, c > 16
d. b < 1, c < 16

Answer 1

To compute the weakest precondition for each assignment statement, we can reverse-engineer the statements and determine the conditions under which the postconditions would hold. In statement (a), the weakest precondition is b > 1.5. In statement (b), the weakest precondition is c > 8. Based on these results, we can determine the weakest preconditions for each option.

Step-by-step explanation:

To compute the weakest precondition for each assignment statement, we need to reverse-engineer the statement and determine the conditions under which the postcondition would hold. Let's start with statement (a):

1. We have the assignment statement a = 2 * (b - 1) - 1 and the postcondition {a > 0}.
2. We want to find the weakest precondition such that when the assignment statement is executed, the postcondition would hold.
3. If a > 0 after the assignment, then we can deduce that 2 * (b - 1) - 1 > 0.
4. Simplifying the inequality, we get b > 1.5.
5. So, the weakest precondition for statement (a) and its postcondition is b > 1.5.

We can follow a similar process for statement (b) to find its weakest precondition.

1. We have the assignment statement b = (c + 10) / 3 and the postcondition {b > 6}.
2. We want to find the weakest precondition such that when the assignment statement is executed, the postcondition would hold.
3. If b > 6 after the assignment, then we can deduce that (c + 10) / 3 > 6.
4. Simplifying the inequality, we get c + 10 > 18.
5. So, the weakest precondition for statement (b) and its postcondition is c > 8.

Based on the above calculations, we can now determine the weakest preconditions for the given options:

1. Option a: b > 1.5, c > 8
2. Option b: b > 1.5, c < 8
3. Option c: b < 1.5, c > 8
4. Option d: b < 1.5, c < 8