MCS-388 Homework 1 (Spring 2000)
Due: February 14, 2000
-
Using the grammar for expr on page 32, show the parse tree
for 5+2*(3+4), where each of the digits (5, 2, 3, 4) is a
digit.
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For the grammar of problem 2.2b on page 78, prove the following:
-
The excess of
a
's over operators (+
's and
-
's) in any S (i.e., any string derivable from
S) is 1.
-
The excess of
a
's over operators in any proper prefix of
an S is less than 1. (If there are more operators than
a
's, the excess is negative. A proper prefix means a
prefix that is not empty and is not the entire string. The
restriction to non-empty prefixes isn't needed here, since the excess
in an empty prefix is of course 0.)
-
The grammar is unambiguous.
-
Do problem 2.5 on page 79.
Course web site: http://www.gac.edu/~max/courses/S2000/MCS-388/
Instructor: Max Hailperin <max@gac.edu>