关于文法的跟随集

Question

Here http://slkpg.byethost7.com/llkparse.html the FOLLOW_k-Sets are defined

"The FOLLOWk set of a string of symbols in a grammar is a set of k-length terminal symbol strings in the grammar that may follow the string of symbols in some sentential form derivable in the grammar"

First i have a quation regarding the example under the link, there for Grammar 4.2

     A  -->  a <Baa> a a              
     A  -->  b <Bba> b a
 <Baa>  -->  b
 <Baa>  -->
 <Bba>  -->  b
 <Bba>  -->

It is said that:

FIRST2 ( A ) = { aa, ab, bb }
FIRST2 ( <Baa> ) = { epsilon }
FIRST2 ( <Bba> ) = { epsilon }

FOLLOW2 ( <Baa> ) = { aa }
FOLLOW2 ( <Bba> ) = { ba }

But i am asking myself why not

FIRST2 ( <Baa> ) = { epsilon, b }
FIRST2 ( <Bba> ) = { epsilon, b }

because from for example also a single b could be derived.

Furthermore for the grammar

S -> X 
X -> aX
X -> aY
Y -> epsilon

i am unsure of the set

FOLLOW2(S)

is it empty, { epsilon } , or { a, aa } because these string are derivable, or is it just important what comes after S, and because S is the startsymbol nothing comes behind it, but then should i write FOLLOW2(S) = \\empyset or FOLLOW2(S) = { epsilon }?

Answer 1

FOLLOWk(S) is empty for any k, because nothing can follow S at all. I don't know what you mean by 'because these strings are derivable', but as they cannot follow S it's irrelevant anyway.