Virtual Labs

Demonstration of Ambiguity in Context-Free Grammars

What is ambiguity in context-free grammars?

a: Having multiple production rules for the same non-terminal Explanation

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b: Having more than one parse tree for the same string Explanation

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c: Having both terminal and non-terminal symbols Explanation

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d: Having recursive production rules Explanation

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In the expression 'id + id * id', what makes the grammar E → E + E | E * E | id ambiguous?

a: The expression contains multiple operators Explanation

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b: The grammar doesn't specify operator precedence Explanation

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c: The expression has too many identifiers Explanation

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d: The grammar is missing parentheses rules Explanation

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What is a parse tree?

a: A sequence of production rule applications Explanation

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b: A tree structure showing how a string is derived from the start symbol Explanation

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c: A list of terminal symbols in a string Explanation

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d: A representation of the grammar's production rules Explanation

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For the grammar S → SS | ab | ba, why is the string 'abab' ambiguous?

a: Because it contains both 'ab' and 'ba' patterns Explanation

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b: Because it can be grouped as (ab)(ab) or as a(ba)b Explanation

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c: Because it can be grouped as (ab)(ab) or as (abab) Explanation

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d: Because it violates the grammar rules Explanation

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What is the 'dangling else' problem in programming languages?

a: When an else statement has no corresponding then statement Explanation

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b: When it's unclear which if statement an else clause belongs to Explanation

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c: When else statements are written incorrectly Explanation

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d: When there are too many nested if statements Explanation

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In a side-by-side derivation comparison, what are you observing?

a: Two different strings being derived Explanation

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b: Two different grammars generating strings Explanation

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c: Two different parse trees for the same string Explanation

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d: Two different types of derivations (leftmost vs rightmost) Explanation

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In the arithmetic expression E → E + E | E * E | (E) | id, if 'id + id * id' is parsed as E[E[id] + E[E[id] * E[id]]], what does this represent?

a: Multiplication has higher precedence than addition Explanation

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b: Addition has higher precedence than multiplication Explanation

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c: Both operators have equal precedence Explanation

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d: The expression is invalid Explanation

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For the if-then-else grammar with the string 'if E then if E then other else other', what causes the ambiguity?

a: The presence of two if statements Explanation

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b: The single else clause can associate with either if statement Explanation

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c: The else clause appears at the end Explanation

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d: The grammar doesn't allow nested if statements Explanation

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When stepping through ambiguous derivations, what pattern would you observe in the derivation steps?

a: Both derivations apply exactly the same rules in the same order Explanation

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b: The derivations apply different rules at certain steps, leading to different tree structures Explanation

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c: One derivation uses more steps than the other Explanation

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d: The derivations generate different final strings Explanation

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