Ambiguity in grammars in Compiler Design - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Identifying Ambiguity in a Grammar

Consider the grammar with rules:

S → aSb | ab

Is this grammar ambiguous?

A No, because each string generated has a unique parse tree.

B No, because the grammar only produces strings of length 2.

C Yes, because the grammar generates infinite strings.

D Yes, because the string 'aabb' can have two different parse trees.

💡 Hint

Try to draw parse trees for strings like 'ab' and 'aabb'.

This grammar generates strings with equal numbers of 'a's followed by equal numbers of 'b's. The string 'aabb' can be derived in more than one way, so the grammar is ambiguous.

📋 Factual

intermediate

Definition of Ambiguous Grammar

Which of the following best defines an ambiguous grammar?

A A grammar that cannot generate any string.

B A grammar that generates at least one string with multiple distinct parse trees.

C A grammar that generates only one string.

D A grammar that has no terminal symbols.

💡 Hint

Think about what ambiguity means in terms of parse trees.

An ambiguous grammar is one where at least one string can be generated in more than one way, resulting in multiple parse trees.

🔍 Analysis

advanced

Ambiguity in Expression Grammar

Given the grammar:

E → E + E | E * E | (E) | id

What is the main cause of ambiguity in this grammar?

A Lack of operator precedence and associativity rules.

B The use of parentheses in expressions.

C The presence of the terminal 'id'.

D The grammar does not generate any strings.

💡 Hint

Consider how expressions like 'id + id * id' can be parsed differently.

The grammar is ambiguous because it does not specify operator precedence or associativity, so expressions can be parsed in multiple ways.

❓ Comparison

advanced

Comparing Ambiguous and Unambiguous Grammars

Which statement correctly compares ambiguous and unambiguous grammars?

A Ambiguous grammars can generate strings with multiple parse trees; unambiguous grammars cannot.

B Unambiguous grammars generate no strings; ambiguous grammars generate all strings.

C Unambiguous grammars always have fewer production rules than ambiguous grammars.

D Ambiguous grammars always generate fewer strings than unambiguous grammars.

💡 Hint

Focus on the number of parse trees per string.

Ambiguous grammars allow multiple parse trees for some strings, while unambiguous grammars have exactly one parse tree per string.

❓ Reasoning

expert

Detecting Ambiguity in a Complex Grammar

Consider the grammar:

S → aSbS | bSaS | ε

Which of the following is true about this grammar?

A It is unambiguous because every string has a unique parse tree.

B It is ambiguous because it generates only the empty string.

C It is ambiguous because the string 'abab' can be derived in two different ways.

D It is unambiguous because it does not generate any strings.

💡 Hint

Try to find two different parse trees for the string 'abab'.

The grammar is ambiguous because the string 'abab' can be derived using different parse trees due to the recursive rules.