Question

1. 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}

1. Prove that the following grammar is ambiguous (show 2 trees):

<S> → <A>

<A> → <A> + <A> | <id>

<id> → a | b | c

Answer 1

1) i)

a = 2 * (b - 1) - 1 {a > 0}

2 * (b - 1) - 1 > 0

2 * (b - 1) > 1

(b - 1) > 1/2

b > 1/2 + 1

b > 3 / 2

Above is the weakest pre-condition.

1) ii)

b = (c + 10) / 3 {b > 6}

(c + 10) / 3 > 6

(c + 10) > 18

c > 18 - 10

c > 8

Above is the weakest pre-condition.

2)

Above are two parse trees for deriving a string aaa. So, it is ambiguous.

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