Are these context free grammars equivalent?

Question

The language is {w|w has an odd length} and the alphabet is {0,1}.

I came up with a solution of

S->1p|0p|e

p->00p|11p|01p|10p|e

and the book has

S->0|1|0S0|0S1|1S0|1S1

are these equivalent?

score 2 · Answer 1 · answered Apr 12 '15 at 20:59

2

They are not. The first grammar describes a language that includes the empty string; e should not be an option for expanding S.

answered Apr 12 '15 at 20:59

user2357112

if e was not included would they be equivalent? – TemporaryFix Apr 12 '15 at 21:00
@Programatic: They would. – user2357112 Apr 12 '15 at 21:01

1 Answers1