Virtual Labs

Equivalence of PA and CFG

After completing the PDA-CFG equivalence simulation, what is the most important insight about these two models?

a: PDAs are always more efficient than CFGs Explanation

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b: Both models recognize identical languages through different computational approaches Explanation

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c: CFGs are easier to implement than PDAs Explanation

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d: The models are only equivalent for simple languages Explanation

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How does observing parallel execution in both models reinforce understanding of equivalence?

a: It shows that one model is faster than the other Explanation

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b: It demonstrates that both models make identical decisions at each step Explanation

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c: It reveals how different computational mechanisms can achieve the same language recognition Explanation

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d: It proves that the models use the same algorithm Explanation

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What does the step-by-step correspondence between PDA transitions and CFG productions demonstrate?

a: That the models execute in exactly the same way Explanation

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b: That there's a systematic relationship between operational and generative approaches Explanation

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c: That one model is derived from the other Explanation

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d: That both models have the same time complexity Explanation

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How does the stack depth in PDA execution relate to CFG derivation complexity?

a: Stack depth is unrelated to CFG properties Explanation

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b: Deeper stacks indicate more complex derivation trees Explanation

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c: Stack depth corresponds to the number of production rules used Explanation

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d: CFG complexity is independent of PDA stack behavior Explanation

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When a PDA makes an epsilon transition, what does this correspond to in the CFG model?

a: Applying a production rule with a terminal on the right side Explanation

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b: Skipping a derivation step Explanation

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c: Applying an ε-production or completing a derivation branch Explanation

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d: Starting a new derivation sequence Explanation

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What advantage does understanding PDA-CFG equivalence provide for parsing algorithm design?

a: It eliminates the need for different parsing strategies Explanation

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b: It allows choosing between operational and generative approaches based on requirements Explanation

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c: It guarantees that all parsing can be done in linear time Explanation

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d: It proves that regular expressions are sufficient for all parsing Explanation

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How does experiencing both models help understand the concept of computational equivalence?

a: By showing that only one model is actually needed Explanation

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b: By demonstrating that equivalent power can be achieved through different computational paradigms Explanation

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c: By proving that all computational models are equivalent Explanation

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d: By showing that simulation is the only way to prove equivalence Explanation

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What does the ability to switch between PDA and CFG views during execution demonstrate about language theory?

a: That one model is more fundamental than the other Explanation

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b: That languages have multiple valid computational representations Explanation

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c: That conversion between models is always possible Explanation

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d: That all formal languages can be expressed in multiple ways Explanation

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How does this experiment's validation system reinforce learning about formal verification?

a: By showing that only one correct answer exists for each step Explanation

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b: By demonstrating how theoretical correctness can be computationally verified Explanation

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c: By proving that formal systems are always deterministic Explanation

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d: By eliminating the need for mathematical proofs Explanation

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