Answers to Self-Study Questions

Test Yourself #1

S → id = id
S → id ( )
S → id ++
S → read ( id )
S → S S

There are no epsilon or unit rules. First, we'll handle rules with terminals on the right, converting the CFG to the following:

S → I A I
S → I L R
S → I P
S → D L I R
S → S S

I → id
A → =
L → (
R → )
P → ++
D → read

Next we'll handle the rules with more than one nonterminal on the right, converting the CFG above to the following:

S → I W
S → I X
S → I P
S → D Y
S → S S

W → A I
X → L R
Y → L Z
Z → I R

I → id
A → =
L → (
R → )
P → ++
D → read

Test Yourself #2

Test Yourself #3

Yes, the input x ++ y = z y ++ is in the language of the simple statement grammar. We know this because the grammar's start nonterminal, S, is in the upper-right corner of the grid.