COMP 412 Fall 2008
Homework 2 Due: Monday, Oct 6th
Problem 1 (20 points)
Consider the grammar
Sโ(L)|a
LโL , S |S
(a) What are the terminals, nonterminals and start symbol?
(b) Find parse trees for the following sentences:
i) (a, a)
ii) (a, (a, a))
(c) Construct the leftmost derivation for each of the sentences in (b)
(d) Construct the rightmost derivation for each of the sentences in (b)
Problem 2 (20 points)
Consider the grammar
SโaSbS |bS aS |๎
(a) Show the grammar is ambiguous by constructing two different leftmost derivations for
the sentence abab.
(b) Construct the corresponding rightmost derivations for abab.
(c) Construct the corresponding parse trees from parts (a) and (b) for abab.
(d) What can you conclude from the parse trees in part (d)?
Problem 3 (20 points)
A grammar symbol Xis defunct if there is no derivation of the form SโโwXy โโwxy,
where XโVand w, x, y โฮฃโ. That is, Xcan never appear in the derivation of some
sentence.
(a) Write an algorithm to eliminate all productions containing defunct symbols from the
grammar.
(b) Apply your algorithm to the grammar below. Describe the steps your algorithm takes.
Sโ0|A
AโAB
Bโ1
1
