What happens when all productions in a grammar are useless?

Asked Nov 04 '15 at 18:00

Active Nov 04 '15 at 18:00

Viewed 36 times

I have this grammar, and I've been asked to eliminate all useless productions.

S-> aS | AB
A-> bA
B-> AA

Now it's pretty easy to see that every production is useless because none of them produce terminal strings. So does this just result in an empty language?

asked Nov 04 '15 at 18:00

Talen Kylon

1

Yes, the language of this grammar is $\varnothing$. – Brian M. Scott Nov 04 '15 at 18:06
@BrianM.Scott Is saying that the language of this grammar is lambda the same thing? – Talen Kylon Nov 04 '15 at 18:09
1

No: ${\lambda}$ is the one-word language whose only word is the empty word, while $\varnothing$ is the language with no words at all. – Brian M. Scott Nov 04 '15 at 18:16
1

That's what I was thinking as well, but wanted to be sure. Cheers! @BrianM.Scott – Talen Kylon Nov 04 '15 at 18:26

What happens when all productions in a grammar are useless?

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