Context-Free Grammar

Question

I need help understanding this concept.

The book states

G1:
    A→0A1
    A→B
    B→#

it states that G1 generates the string 000#111

and shows a process

A → 0A1 → 00A11 → 000A111 → 000B111 → 000#111

I understand what is happening in here. What I'm unsure of is if it can be infinitely looped.

For example:

can G1 also generate 0#1 using this process

A → 0A1 → 0B1 → 0#1

The book doesn't explain this part as clearly. Thanks

Answer 1

Yes, any production can be applied an infinite number of times, thereby generating (in this and in most cases) an infinite number of strings. This grammar generates all strings of the form 0ⁿ#1ⁿ

Answer 2

Yes surely. The given grammar also generates the 0#1 language. The thing is clear enough. As you can see , the generated language 0#1 is a subset of the former language generated by the same grammar.