Ambiguity in grammars in Compiler Design - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does it mean when a grammar is ambiguous?

A grammar is ambiguous if there is at least one string that can be generated in more than one way, meaning it has more than one distinct parse tree or derivation.

beginner

Why is ambiguity in grammars a problem in compiler design?

Ambiguity causes confusion in understanding the structure of code, making it hard for compilers to decide which meaning or parse tree to use, leading to incorrect program interpretation.

intermediate

Give a simple example of an ambiguous grammar.

The grammar with rules: E → E + E | E * E | id is ambiguous because the expression 'id + id * id' can be parsed in two different ways, changing the order of operations.

beginner

What is a parse tree and how does it relate to ambiguity?

A parse tree shows how a string is derived from a grammar. Ambiguity means there is more than one valid parse tree for the same string.

intermediate

How can ambiguity in grammars be resolved?

Ambiguity can be resolved by rewriting the grammar to remove multiple interpretations, often by adding precedence rules or using unambiguous grammar forms.

What does ambiguity in a grammar mean?

A A string can have multiple parse trees

B Grammar has syntax errors

C Grammar cannot generate any string

D Grammar has only one production rule

Ambiguity means a string can be generated in more than one way, resulting in multiple parse trees.

Which of the following is a sign of an ambiguous grammar?

A Multiple parse trees for the same string

B No parse tree for any string

C Only one production rule

D Grammar is context-free

Ambiguous grammars allow multiple parse trees for the same string.

Why is ambiguity bad for compilers?

A It reduces code size

B It makes code run faster

C It causes confusion in interpreting code

D It helps optimize code

Ambiguity makes it unclear how to interpret code, causing errors in compilation.

Which expression shows ambiguity in the grammar E → E + E | E * E | id?

A id

B id + id

C id * id

D id + id * id

The expression 'id + id * id' can be parsed in two ways, showing ambiguity.

How can ambiguity be removed from a grammar?

A Remove all production rules

B Rewrite grammar with precedence rules

C Add more ambiguous rules

D Ignore ambiguity

Adding precedence rules or rewriting the grammar helps remove ambiguity.

Explain what ambiguity in grammars means and why it matters in compiler design.

Think about how one string can be understood in different ways.

Describe a simple example of an ambiguous grammar and how you might fix it.

Consider arithmetic expressions with + and * operators.

Practice

1. What does ambiguity in a grammar mean?

easy

A. A sentence can have more than one meaning

B. The grammar has no rules

C. All sentences are correct

D. The grammar is too simple

Solution

1. Step 1: Understand the definition of ambiguity in grammar

   Ambiguity means a sentence can be interpreted in multiple ways within the grammar.

2. Step 2: Compare options with the definition

   Only A sentence can have more than one meaning correctly states that ambiguity means multiple meanings for a sentence.

3. Final Answer:

   A sentence can have more than one meaning -> Option A

4. Quick Check:

   Ambiguity = Multiple meanings [OK]

Hint: Ambiguity means multiple meanings for one sentence [OK]

Common Mistakes:

• Confusing ambiguity with grammar errors
• Thinking ambiguity means no rules
• Assuming ambiguity means all sentences are correct

2. Which of the following grammar rules is ambiguous?

easy

A. S -> aSb | ab

B. S -> aS | b

C. S -> aSb | aSb

D. S -> ab | ba

Solution

1. Step 1: Analyze the grammar rules for ambiguity

   Rule A allows multiple parse trees for strings like 'aabb', causing ambiguity.

2. Step 2: Check other options for ambiguity

   Options B, C, and D do not produce multiple parse trees for the same string.

3. Final Answer:

   S -> aSb | aSb -> Option C

4. Quick Check:

   Multiple parse trees = Ambiguous [OK]

Hint: Look for rules generating multiple parse trees [OK]

Common Mistakes:

• Ignoring repeated rules that cause ambiguity
• Confusing ambiguity with grammar repetition
• Assuming all recursive rules are ambiguous

3. Given the grammar:
E -> E + E | E * E | id
What is the ambiguity in parsing the expression id + id * id?

medium

A. The expression cannot contain '*'

B. The expression is invalid

C. The expression has only one parse tree

D. The expression can be parsed as (id + id) * id or id + (id * id)

Solution

1. Step 1: Understand the grammar's ambiguity

   The grammar allows both '+' and '*' without precedence rules, causing multiple parse trees.

2. Step 2: Analyze the expression parsing

   The expression 'id + id * id' can be parsed as either 'id + (id * id)' or '(id + id) * id', showing ambiguity.

3. Final Answer:

   The expression can be parsed as (id + id) * id or id + (id * id) -> Option D

4. Quick Check:

   Multiple parse trees = Ambiguity [OK]

Hint: Check if operator precedence is missing [OK]

Common Mistakes:

• Assuming only one parse tree exists
• Ignoring operator precedence
• Thinking expression is invalid

4. Identify the error in this ambiguous grammar and suggest a fix:
S -> S + S | S * S | id

medium

A. Ambiguity due to missing operator precedence; fix by defining precedence rules

B. No error, grammar is unambiguous

C. Grammar is invalid syntax; fix by removing recursion

D. Ambiguity due to missing terminals; fix by adding more terminals

Solution

1. Step 1: Identify the cause of ambiguity

   The grammar allows multiple parse trees because it lacks operator precedence rules.

2. Step 2: Suggest a fix

   Define separate rules for '+' and '*' with precedence to remove ambiguity.

3. Final Answer:

   Ambiguity due to missing operator precedence; fix by defining precedence rules -> Option A

4. Quick Check:

   Missing precedence = Ambiguity fix [OK]

Hint: Add precedence rules to fix ambiguity [OK]

Common Mistakes:

• Thinking recursion causes ambiguity
• Assuming grammar syntax is invalid
• Ignoring operator precedence importance

5. How can ambiguity be resolved in a grammar that allows multiple parse trees for the same sentence?

hard

A. By allowing multiple parse trees

B. By rewriting the grammar to enforce operator precedence and associativity

C. By removing all terminals

D. By adding more recursive rules

Solution

1. Step 1: Understand the cause of ambiguity

   Ambiguity arises when the grammar allows multiple parse trees for the same sentence.

2. Step 2: Apply a solution

   Rewriting the grammar to include operator precedence and associativity rules removes ambiguity.

3. Final Answer:

   By rewriting the grammar to enforce operator precedence and associativity -> Option B

4. Quick Check:

   Rewrite grammar with precedence = Resolve ambiguity [OK]

Hint: Use precedence and associativity rules to fix ambiguity [OK]

Common Mistakes:

• Adding recursion increases ambiguity
• Removing terminals breaks grammar
• Accepting ambiguity as normal