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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 Spring '09
 InessaEpstein
 Math, Formal grammar, grammatically correct strings, parse tree TA

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