Consider the grammar with non-terminals N = {S,C,S1 },terminals T={a,b,i,t,e},…

2007

Consider the grammar with non-terminals N = {S,C,S1 },terminals T={a,b,i,t,e}, with S as the start symbol, and the following set of rules:

S --> iCtSS1|a
S1 --> eS|ϵ
C --> b

The grammar is NOT LL(1) because:

  1. A.

    it is left recursive

  2. B.

    it is right recursive

  3. C.

    it is ambiguous

  4. D.

    It is not context-free.

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Show answer & explanation

Correct answer: C

Correct reason: there is a FIRST/FOLLOW conflict for the nonterminal S1, so a single-token lookahead cannot always choose the right production.

  • Productions:

    • S → i C t S S1

    • S → a

    • S1 → e S

    • S1 → ε

    • C → b

Compute FIRST sets:

  • FIRST(S) = {i, a}

  • FIRST(S1) = {e, ε}

  • FIRST(C) = {b}

Compute FOLLOW sets (key points):

  • S is the start symbol, so $ ∈ FOLLOW(S).

  • In the production S → i C t S S1, the S that appears before S1 has FIRST(S1) − {ε} = {e} in its FOLLOW. Because S1 can be ε, FOLLOW(S) (which contains $) is also in FOLLOW of that S. Hence FOLLOW(S) = {e, $}.

  • S1 appears at the end of the S production, so FOLLOW(S1) = FOLLOW(S) = {e, $}.

Why this causes a conflict:

  • For nonterminal S1 we have two alternatives: one starts with terminal e (FIRST = {e}) and the other is ε (FIRST contains ε).

  • Because ε is an alternative, the parser must consult FOLLOW(S1) to decide when to use the ε-production. But FOLLOW(S1) contains e, and e is also in FIRST of the other alternative.

  • Therefore FIRST(e S) ∩ FOLLOW(S1) contains e, creating a predictive parsing table conflict. This makes the grammar not LL(1).

Additional clarifications:

  • This is a FIRST/FOLLOW conflict, not necessarily ambiguity. Ambiguity is a different property (multiple parse trees for the same string).

  • The grammar is context-free and not left-recursive, so the listed reasons claiming non-context-freeness or left recursion are incorrect.

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