How do I solve this? The answer is the well-formed formula is incorrect when $x = -1$ and $y = -1$. Can someone explain to me why that is the answer?
{True} If x < y then y:= y - x {y>0}
Show that the following well-formed formula is not correct over the domain of integers?
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discrete-mathematics
logic
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0What is "wfff"? Could someone clarify? – 2017-02-23
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0well-formed-formula – 2017-02-23
1 Answers
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{True} If x < y then y:= y - x {y>0} is a Hoare triple, in which {True} is the precondition, {y>0} is the postcondition, and If x < y then y:= y - x is the command. The question is whether assuming the precondition holds before the command is carried out, the postcondition is then guaranteed to hold.
Since the precondition is unconditionally satisfied, nothing is assumed about the values of x and y. In particular, as suggested by the solution key, it may be that x = y = -1. If that's the case the guard x < y is false, and the assignment y := y - x does not take place. Hence, x and y keep their values, which violate the postcondition y > 0.
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0would this violate also if x and y were say -5? – 2017-02-23
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0Yes, it would. Once you figure out how it works you can find as many counterexamples as you want. Another would be $x = -1$ and $y = -5$. As long as $y \leq 0$ and $x \geq y$ before the if statement, the postcondition does not hold. – 2017-02-23
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0your answer isnt correct?!?! – 2017-02-23