Final answer:
To remove direct left recursion, we follow the algorithm described in Section 4.4.2. To remove left recursion from the given grammar rules, α substrings (a, abc) and β substrings (bc, d) are identified. The new A-rules (A → bc A' | d A') and A'-rules (A' → a A' | abc A' | ε) are established to eliminate direct left recursion.
Step-by-step explanation:
In order to remove direct left recursion from the given grammar rules, we need to follow the algorithm described in Section 4.4.2.
- First, we identify the α (alpha) and β (beta) substrings in each A-rule.
- Next, we create new A-rules and A'-rules based on the α and β substrings.
Using the given grammar rules: A → Aa | Abc | bc | d
- The α substrings are: ε (empty), and 'bc'
- The β substrings are: 'a' and 'bc'
- The new A-rules and A'-rules are:
- A → Aa | A'
- A' → bc | ε
Therefore, the direct left recursion has been removed from the grammar rules.
To remove left recursion from the given grammar rules, α substrings (a, abc) and β substrings (bc, d) are identified. The new A-rules (A → bc A' | d A') and A'-rules (A' → a A' | abc A' | ε) are established to eliminate direct left recursion.
To remove direct left recursion from the given grammar rules, we need to identify the α (alpha) and β (beta) substrings where α represents the recursive productions and β the non-recursive ones. Given the grammar rule A → Aa | Abc | bc | d, we have:
α substrings: a, abc
β substrings: bc, d
To transform the grammar to remove left recursion we introduce a new nonterminal A' and rewrite the original rule as follows:
A-rules: A → β A' (A → bc A' | d A')
A'-rules: A' → α A' | ε (A' → a A' | abc A' | ε)
Here, ε represents the empty string. The transformed rules ensure that recursive calls to A are now only made from A', effectively removing direct left recursion.