📘 1. Ambiguity in Grammar

✅ Definition

A grammar is ambiguous if a single string can have more than one parse tree (or derivation).

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📌 Example Grammar

E → E + E | E * E | id

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🎯 String:

id + id * id

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❗ Problem

This string can be interpreted in two different ways:

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🔹 Interpretation 1:

(id + id) * id

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🔹 Interpretation 2:

id + (id * id)

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🌳 Two Parse Trees (Conceptual)

Tree 1:

       E
     / | \
    E  *  E
   /|\     |
  E + E   id
  |   |
 id  id

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Tree 2:

       E
     / | \
    E  +  E
    |     /|\
   id    E * E
         |   |
        id  id

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⚠️ Conclusion

👉 Same input → Different meanings → ❌ Ambiguity

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⭐ Key Points (Exam)

• Ambiguous grammar → more than one parse tree
• Not suitable for compiler design
• Must be removed

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🧠 2. Associativity of Operators

✅ Definition

Associativity defines the order in which operators of the same precedence are evaluated.

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🔄 Types of Associativity

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🔹 1. Left Associativity

👉 Evaluation from left to right

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📌 Example:

a - b - c

👉 Interpreted as:

(a - b) - c

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⭐ Operators

• +, -, *, /

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🔹 2. Right Associativity

👉 Evaluation from right to left

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📌 Example:

a = b = c

👉 Interpreted as:

a = (b = c)

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⭐ Operators

• Assignment (=)
• Exponentiation (^)

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🎯 Key Points (Exam)

• Same operator → associativity decides order
• Left vs Right is very important

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🧠 3. Precedence of Operators

✅ Definition

Precedence defines which operator is evaluated first when different operators appear together.

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📌 Example

a + b * c

👉 Multiplication has higher precedence:

a + (b * c)

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📊 Common Precedence Order

Level	Operator	Meaning
High	^	Power
Medium	*, /	Multiply/Divide
Low	+, -	Add/Subtract
Lowest	=	Assignment

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⭐ Key Points (Exam)

• Higher precedence → evaluated first
• Reduces ambiguity
• Used in grammar design

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🔄 4. Removing Ambiguity Using Precedence & Associativity

📌 Ambiguous Grammar

E → E + E | E * E | id

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✅ Unambiguous Grammar

E → E + T | T
T → T * F | F
F → id

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🧠 Explanation

• * has higher precedence than +
• Grammar enforces correct evaluation

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🔗 5. Relationship Between Concepts

Ambiguity → Resolved by → Precedence + Associativity

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🧪 6. Complete Example

Expression:

a + b * c - d

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Step-by-Step Evaluation

1. * first → b * c
2. + and - left to right

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Final Form:

((a + (b * c)) - d)

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⚠️ 7. Common Mistakes

• Ignoring precedence
• Confusing associativity
• Writing ambiguous grammar

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🎯 8. Important Exam Concepts

👉 Frequently asked:

• Define ambiguity with example
• Draw multiple parse trees
• Define associativity (left/right)
• Define precedence with examples
• Remove ambiguity from grammar
• Difference between precedence and associativity

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📝 9. Short Notes (Quick Revision)

Ambiguity

• Multiple parse trees
• Must be removed

Associativity

• Same operator order
• Left or right

Precedence

• Priority of operators
• Higher evaluated first

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📊 10. Final Summary Table

Aspect	Ambiguity	Associativity	Precedence
Definition	Multiple parse trees	Order for same operators	Priority of operators
Purpose	Identify problem	Resolve order	Resolve priority
Example	id + id * id	a - b - c	a + b * c
Type	—	Left/Right	Levels
Role	Problem	Solution	Solution
Importance	Very High	Very High	Very High

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✅ Final Conclusion

• Ambiguity creates confusion in parsing ❌
• Associativity and precedence resolve that confusion ✅
• Proper grammar design ensures correct evaluation of expressions

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