CMSC 330
Practice Problems 3
For this exercise, weโll call a backtracking recursive-
descent parser a backtracking parser, and a non-
backtracking recursive-descent parser a predic-
tive parser.
1. Consider the grammar
SโABd |aBc
Aโ๎
Bโb|c
(a) Compute First sets for each produc-
tion
(b) Can the grammar be parsed by a pre-
dictive parser?
(c) Implement a predictive parser for the
grammar
(d) Use your parser to parse the strings
โbdโ and โaccโ. Show the sequence
of procedure calls in the parse, and
what symbols remain to be parsed at
each point.
2. Consider the grammar
SโAS |b
AโSA |a
(a) Compute First sets for each produc-
tion
(b) Can the grammar be parsed by a pre-
dictive parser?
(c) Can the grammar be parsed by a back-
tracking parser?
(d) Is the grammar ambiguous? Prove your
answer.
(e) Are all ambiguous grammars non-parseable
by predictive parsers?
(f) Are all non-ambiguous grammars parseable
by predictive parsers?
3. Consider the grammar
Sโ(L)|a
LโL , S |S
(a) Compute First sets for each produc-
tion
(b) Can the grammar be parsed by a pre-
dictive parser?
(c) Can the grammar be parsed by a back-
tracking parser?
(d) Rewrite grammar using the rule for
eliminating left recursion
(e) Compute First sets for each produc-
tion
(f) Can the resulting grammar be parsed
by a predictive parser?
(g) Write a predictive parser for the gram-
mar
(h) Use your parser to parse the string
โ(a,a)โ. Show the sequence of calls in
the parse, and what symbols remain
to be parsed at each point.
4. Consider the grammar
EโE + T |T
Tโa|(E)
(a) Compute First sets for each produc-
tion
(b) Is the grammar ambiguous?
(c) Can the grammar be parsed by a pre-
dictive parser?
(d) Can the grammar be parsed by a back-
tracking parser?
(e) Rewrite grammar using the rule for
eliminating left recursion
(f) Compute First sets for each produc-
tion
(g) Can the resulting grammar be parsed
by a predictive parser?
(h) Write a predictive parser for the gram-
mar
(i) Use your parser to parse the string โa
+ a + aโ.
