Ambiguity in grammars in Compiler Design - Step-by-Step Execution

Concept Flow - Ambiguity in grammars

Start with Grammar

↓

Parse Input String

↓

Generate Parse Trees

↓

Check Number of Parse Trees

↓

One

↓

Unambiguous

The process starts with a grammar and input string, then generates parse trees. If there is more than one valid parse tree for the same input, the grammar is ambiguous.

Execution Sample

Compiler Design

Grammar:
S -> S + S | a
Input: a + a + a

This grammar can generate multiple parse trees for the input 'a + a + a', showing ambiguity.

Analysis Table

Step	Input Processed	Parse Tree Count	Action	Result
1	a	1	Parse 'a' as S	One parse tree for 'a'
2	a + a	1	Parse 'a + a' as S + S	One parse tree: (a + a)
3	a + a + a	2	Parse 'a + a + a' as (S + S) + S or S + (S + S)	Two different parse trees for full input
4	Check parse trees	2	More than one parse tree found	Grammar is ambiguous

💡 Parsing stops because multiple parse trees exist for the input, indicating ambiguity.

State Tracker

Variable	Start	After 1	After 2	After 3	Final
Parse Tree Count	0	1	1	2	2

Key Insights - 2 Insights

Why does the parse tree count increase at step 3?

At step 3, the input 'a + a + a' can be parsed in two ways due to the recursive rule S -> S + S, creating two parse trees as shown in execution_table row 3.

Does having multiple parse trees mean the input is invalid?

No, multiple parse trees mean the grammar is ambiguous for that input, not that the input is invalid. This is shown in execution_table row 4.

Visual Quiz - 3 Questions

According to the execution_table, how many parse trees exist after processing 'a + a'?

A 3

B 1

C 2

D 0

💡 Hint

Look at execution_table row 2 under 'Parse Tree Count' column.

At which step does the grammar get identified as ambiguous?

A Step 1

B Step 2

C Step 4

D Step 3

💡 Hint

Check execution_table row 4 where the action notes multiple parse trees found.

If the grammar had only one parse tree at every step, what would the 'Parse Tree Count' be in variable_tracker's final column?

A 1

B 0

C 2

D Multiple

💡 Hint

Refer to variable_tracker row for 'Parse Tree Count' and imagine only one parse tree at each step.

Concept Snapshot

Ambiguity in grammars means an input string can have multiple valid parse trees.
Check parse trees generated for input; if more than one, grammar is ambiguous.
Ambiguity causes confusion in parsing and compiler design.
Example: S -> S + S | a with input 'a + a + a' has multiple parse trees.
Avoid ambiguity for clear, deterministic parsing.

Full Transcript

Ambiguity in grammars happens when a single input string can be parsed in more than one way, producing multiple parse trees. Starting with a grammar and an input, we try to parse the input. If we find more than one parse tree, the grammar is ambiguous. For example, the grammar with rules S -> S + S or S -> a can parse 'a + a + a' in two different ways. This is shown step-by-step in the execution table where the parse tree count increases and finally shows ambiguity. Understanding this helps in designing clear grammars for compilers.

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