Question

4)

Calculate Nullable, FIRST and FOLLOW for nonterminals A and B for the following grammar.

A → BAa

A → ε

B → bBc

B → AA

please help ASAP

Answer 1

Non-terminal N is nullable if N Æ+ ε • Example: S Æ AB$ A Æ a | ε B Æ b • When should you use the A Æ ε production? • One solution: – Ignore ε productions and compute FIRST – Table[A,a] = AÆa – all other entries for A: A Æ ε • This is bad practice – errors should be caught as soon as possible – what if next input token was $? • Solution: – if we use A Æ ε production to derive a legal string, next token in input must be b – if next token is b, use A Æ ε production; otherwise report error • How do we describe this formall

FOLLOW: Non-terminal Æ subset of terminals • b ε FOLLOW(A) if S Æ* …Ab… • To compute FOLLOW(A), we must look at RHS of productions that contain A • Example: S Æ AB$ A Æ a | ε B Æ b • FOLLOW(B) = {$} • FOLLOW(A) = FIRST(B) • But ε rules change FIRST computation as well! – FIRST(S) needs to take into account the fact that A is nullable • How do we get all this straight?