Question

Predictive parse table  for following grammars:
1.S->FR
   R->*S/∈
   F->id

and

2.S->iEtSS' | a
   S'->eS | ∈
   E->b

Answer 1

S->FR 

R->*S/∈ 

F->id

FIRST(S) = FIRST(FR) = FIRST(F) = { id }

For R->*S,  FIRST(R) = { * }

For R->∈ ,  FIRST(R) = { ∈ },  FOLLOW(R) = FOLLOW(S) = { $ }

So both productions will be placed in different column

FIRST(F) = { id }

So above grammer can be parsed by LL(1) and parsing table is as follows:

	*	id	$
S	-	S->FR	-
R	R->*S	-	R->∈
F	-	F->id	-

for 2nd one

S->iEtSS' | a 
S'->eS | ∈ 
E->b

for S->iEtSS', FIRST(S) = { i }

for S->a, FIRST(S) = { a }

for S'->eS, FIRST(S') = { e }

for S'->∈, FIRST(S') = { ∈ } and FOLLOW(S') = FOLLOW(S) = FIRST(S') U { dollar } = { dollar,e }

Since in column e there will be two productions so it cant be parsed using LL(1) parser.

FIRST(E) = { b }

So above grammer cant be parsed by using LL(1) parser