Ma/CS 6c Assignment #1 Due Wednesday, April 7 at 1 p.m. (40%) 1 * . (a) Prove the correctness of the following algorithm for recognizing when a given string S is a P-wﬀ: If S = s 1 s 2 ...s n , compute w ( s n ) ,w ( s n )+ w ( s n-1 ) ,...,w ( s n )+ w ( s n-1 )+ ··· + w ( s 1 ) = w ( S ). If all these sums are ≥ 1 and w ( S ) = 1, then S is a P-wﬀ; otherwise, it is not. (Recall that w ( p ) = 1 , w ( ¬ ) = 0 , w ( * ) =-1, if * = ∧ , ∨ , ⇒ , ⇔ .) Apply this algorithm to the strings: (i) qp ⇒ ¬ ttr ⇒ ∧¬ stuv ; (ii) ⇒⇔ ¬ ∧ pq ∨ ¬ p ¬ qs . If any of these strings is a P-wﬀ, write down the corresponding wﬀ. (40%) 2. Show that unique readability holds for the formal language described below (whose grammatically correct strings we call
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Formal grammar, grammatically correct strings, parse tree TA