一些NFA，常规语言和等效功能

Question

I read some note about Automaton Course. i see this note, that following all is the same. but i think the L(g) is not equal to NFA and regular expression. anyone could help me with defining the language of this figures (nfa, regular expression and grammar):

Answer 1

They are in fact equivalent, but this is a strange way of converting one to the other.

R is the same as (a|b)b* . M recognizes (a|b)(bb)*b? . The right part recognizes 2*n+1 or 2*n b 's, where n>=0 , hence is equivalent to R .

Now on G

A recognizes (bb)*b? , which is equivalent to b* (see comment on M ).

B recognizes bB|bb*|e which is equivalent to bB|b* which is equivalent to b* .

S recognizes ab*b*|bb*b which is equivalent to ab*|bbb* , which is equivalent to (a|bb)b* .