Chapter 2, Problem 14E

Explanation of Solution

a.

Grammar for LL (1):

Consider the grammar for LL (1) as below:

$\begin{array}{l}\text{1}\text{. P }\to \text{ S \$\$}\\ \text{2}\text{. S }\to \left(\text{ S }\right)\text{ S}\\ \text{3}\text{. S }\to \left[\text{ S }\right]\text{ S}\\ \text{4}\text{. S }\to \epsilon \end{array}$

Grammar for SLR (1):

Consider the grammar for SLR (1) as below:

$\begin{array}{l}\text{1}\text{. P }\to \text{ S \$\$}\\ \text{2}\text{. S }\to \text{ S }\left(\text{ S }\right)\\ \text{3}\text{. S }\to \text{ S}\text{}\left[\text{ S }\right]\\ \text{4}\text{. S }\to \epsilon \end{array}$

Explanation of Solution

b.

Parsing table for LL (1) grammar:

Top-of-stack non-terminal	(	)	[	]	$$
P	1	-	1	-	1
S	2	4	3	4	4

• The entries in the above table indicates the production of predict. The “-” means an error.
• If the top-of-stack is terminal, the appropriate action is always to match it against an incoming token from the scanner.

Parsing table for SLR (1) grammar:

Top-of-stack	S	(	)	[	]	$$
0	s1	r4	r4	r4	r4	r4
1	-	s2	-	s3	-	b1
2	s4	r4	r4	r4	r4	r4
3	s5	r4	r4	r4	r4	r4
4	-	s2	b2	s3	-	-
5	-	s2	-	s3	b3	-

• The entries in the above table indicates whether to shift (s), reduce (r), or shift and then reduce (d). The “-” means an error.

Explanation of Solution

c.

Parsing tree for LL (1):

Parsing tree for SLR (1):

Explanation of Solution

d.

LL (1) trace:

Parse stack	Input stream	Comment
P	( [ ] ( [ ] ) ) [ ] ( ( ) ) $$
S $$	( [ ] ( [ ] ) ) [ ] ( ( ) ) $$	Predict P →S $$
( S ) S $$	( [ ] ( [ ] ) ) [ ] ( ( ) ) $$	Predict S →( S ) S
S ) S $$	[ ] ( [ ] ) ) [ ] ( ( ) ) $$	Match (
[ S ] S ) S $$	[ ] ( [ ] ) ) [ ] ( ( ) ) $$	Predict S →[ S ] S
S ] S ) S $$	] ( [ ] ) ) [ ] ( ( ) ) $$	Match [
] S ) S $$	] ( [ ] ) ) [ ] ( ( ) ) $$	Predict S → ε
S ) S $$	( [ ] ) ) [ ] ( ( ) ) $$	Match ]
( S ) S ) S $$	( [ ] ) ) [ ] ( ( ) ) $$	Predict S →( S ) S
S ) S ) S $$	[ ] ) ) [ ] ( ( ) ) $$	Match (
[ S ] S ) S ) S $$	[ ] ) ) [ ] ( ( ) ) $$	Predict S →[ S ] S
S ] S ) S ) S $$	] ) ) [ ] ( ( ) ) $$	Match [
] S ) S ) S $$	] ) ) [ ] ( ( ) ) $$	Predict S → ε
S ) S ) S $$	) ) [ ] ( ( ) ) $$	Match ]
) S ) S $$	) ) [ ] ( ( ) ) $$	Predict S → ε
S ) S $$	) [ ] ( ( ) ) $$	Predict S →
) S $$	) [ ] ( ( ) ) $$	Predict S → ε
S $$	[ ] ( ( ) ) $$	Match )
[ S ] S $$	[ ] ( ( ) ) $$	Predict S →[ S ] S
S ] S $$	] ( ( ) ) $$	Match [
] S $$	] ( ( ) ) $$	Predict S → ε
S $$	( ( ) ) $$	Match ]
( S ) S $$	( ( ) ) $$	Predict S →( S ) S
S ) S $$	( ) ) $$	Match (
( S ) S ) S $$	( ) ) $$	Predict S →( S ) S
S ) S ) S $$	) ) $$	Match (
) S ) S $$	) ) $$	Predict S → ε
S ) S $$	) $$	Match )
) S $$	) $$	Predict S → ε
S $$	$$	Match )
$$	$$	Predict S → ε

SLR (1) trace:

Parse stack	Input stream	Comment
0	( [ ] ( [ ] ) ) [ ] ( ( ) ) $$
0	S ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1	( [ ] ( [ ] ) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2	[ ] ( [ ] ) ) [ ] ( ( ) ) $$	Shift (
0S1 ( 2	S [ ] ( [ ] ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4	[ ] ( [ ] ) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2 S 4 [ 3	] ( [ ] ) ) [ ] ( ( ) ) $$	Shift [
0S1 ( 2 S 4 [ 3	S ] ( [ ] ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4 [ 3 S 5	] ( [ ] ) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2	( [ ] ) ) [ ] ( ( ) ) $$	Shift and reduce by S→ S [ S ]
0S1 ( 2	S ( [ ] ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4	( [ ] ) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2 S 4 ( 2	[ ] ) ) [ ] ( ( ) ) $$	Shift (
0S1 ( 2 S 4 ( 2	S [ ] ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4 ( 2 S 4	[ ] ) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2 S 4 ( 2 S 4 [ 3	] ) ) [ ] ( ( ) ) $$	Shift [
0S1 ( 2 S 4 ( 2 S 4 [ 3	S ] ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4 ( 2 S 4 [ 3 S 5	] ) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2 S 4 ( 2	) ) [ ] ( ( ) ) $$	Shift and reduce by S→ S [ S ]
0S1 ( 2 S 4 ( 2	S ) ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4 ( 2 S 4	) ) [ ] ( ( ) ) $$	Shift S
0S1 ( 2	) [ ] ( ( ) ) $$	Shift and reduce by S→ S ( S )
0S1 ( 2	S ) [ ] ( ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4	) [ ] ( ( ) ) $$	Shift S
0	[ ] ( ( ) ) $$	Shift and reduce by S→ S ( S )
0	S [ ] ( ( ) ) $$	Reduce by S→ ε
0S1	[ ] ( ( ) ) $$	Shift S
0S1 [ 3	] ( ( ) ) $$	Shift [
0S1 [ 3	S ] ( ( ) ) $$	Reduce by S→ ε
0S1 [ 3 S 5	] ( ( ) ) $$	Shift S
0	( ( ) ) $$	Shift and reduce by S→ S [ S ]
0	S ( ( ) ) $$	Reduce by S→ ε
0S1	( ( ) ) $$	Shift S
0S1 ( 2	( ) ) $$	Shift (
0S1 ( 2	S ( ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4	( ) ) $$	Shift S
0S1 ( 2 S 4 ( 2	) ) $$	Shift (
0S1 ( 2 S 4 ( 2	S ) ) $$	Reduce by S→ ε
0S1 ( 2 S 4 ( 2 S 4	) ) $$	Shift S
0S1 ( 2	) $$	Shift and reduce by S→ S ( S )
0S1 ( 2	S ) $$	Reduce by S→ ε
0S1 ( 2 S 4	) $$	Shift S
0	$$	Shift and reduce by S→ S ( S )
0	S $$	Reduce by S→ ε
0S1	$$	Shift S
0	P	Shift and reduce by S→ S ( S )
[done]