The grammar A → AA | (A) | ε is not suitable for predictive-parsing because…

Answer: ambiguous

Explanation:

• The grammar is ambiguous. Simple counterexample: the empty string ε can be derived in at least two different ways:

  • Derivation 1: A ⇒ ε (use A → ε).

  • Derivation 2: A ⇒ AA ⇒ ε ε (use A → AA, then each A → ε).

• Because there are multiple distinct parse trees for the same string, the grammar is ambiguous. Predictive (deterministic top-down) parsing requires a single, unambiguous parse for each sentence, so ambiguity makes the grammar unsuitable.

• The grammar is also immediately left-recursive (A → AA). Immediate left recursion causes infinite recursion in naive top-down parsers and must be removed or transformed for predictive parsing.

• Summary: The primary stated reason is ambiguity (the grammar allows multiple parse trees for some strings). Additionally, immediate left recursion is another problem for predictive parsing.

• A common unambiguous, non-left-recursive grammar for balanced parentheses is:

  • S → (S)S | ε