Question

1.2 The following Hoare triple is invalid: {x > 0} x := x - 1 {x > 0}. Change the Hoare triple to valid by i. defining a stronger precondition ii. defining a weaker postcondition iii. changing the program 1.3 Using the assignment axiom (9.2 of the textbook) determine the precondition for the following statements and postconditions. Where necessary, simplify the precondition | | Precondition | Statement | Postcondition | |---|---|---|---| | i. | | x := x + y | {x < 2 x y} | | ii. | | x : x x y | {x x y = C} | | iii. | | x := x - y | {x > 2} | | iv. | | y := 0 - x | {y < 0 ? x ? y} | | v. | | x := x x 2 + 3 | {x > 1} |

          1.2 The following Hoare triple is invalid: {x > 0} x := x - 1 {x > 0}. Change the Hoare triple to valid by
i. defining a stronger precondition
ii. defining a weaker postcondition
iii. changing the program
1.3 Using the assignment axiom (9.2 of the textbook) determine the precondition for the following statements and postconditions. Where necessary, simplify the precondition
| | Precondition | Statement | Postcondition |
|---|---|---|---|
| i. | | x := x + y | {x < 2 x y} |
| ii. | | x : x x y | {x x y = C} |
| iii. | | x := x - y | {x > 2} |
| iv. | | y := 0 - x | {y < 0 ? x ? y} |
| v. | | x := x x 2 + 3 | {x > 1} |

1.2 The following Hoare triple is invalid: x > 0 x := x - 1 x > 0. Change the Hoare triple to valid by
i. defining a stronger precondition
ii. defining a weaker postcondition
iii. changing the program
1.3 Using the assignment axiom (9.2 of the textbook) determine the precondition for the following statements and postconditions. Where necessary, simplify the precondition
| | Precondition | Statement | Postcondition |
|—|—|—|—|
| i. | | x := x + y | x < 2 x y |
| ii. | | x : x x y | x x y = C |
| iii. | | x := x - y | x > 2 |
| iv. | | y := 0 - x | y < 0 ? x ? y |
| v. | | x := x x 2 + 3 | x > 1 |

Added by Lisa B.

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