Virtual Labs

Equivalence of 2-Stack PDA and DTM

What is the fundamental difference between a single-stack PDA and a 2-stack PDA in terms of computational power?

a: Single-stack PDAs are more powerful because they are simpler Explanation

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b: 2-stack PDAs achieve Turing-complete computational power while single-stack PDAs recognize only context-free languages Explanation

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c: Both have identical computational power, just different memory organization Explanation

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d: Single-stack PDAs can simulate Turing machines while 2-stack PDAs cannot Explanation

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In a Deterministic Turing Machine, what are the three operations that occur in each transition?

a: Read symbol, push to stack, change state Explanation

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b: Read symbol, write symbol, move head Explanation

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c: Write symbol, move head, change state Explanation

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d: Read symbol, write symbol, move head, and change state Explanation

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For the w#w language recognition problem, what is the primary role of the separator symbol '#'?

a: It marks the end of the input string Explanation

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b: It serves as a delimiter between two parts that must be identical Explanation

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c: It represents a wildcard that can match any character Explanation

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d: It indicates where the machines should start processing Explanation

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How does a 2-stack PDA simulate the tape of a Turing machine?

a: One stack stores the entire tape contents Explanation

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b: Both stacks store identical copies of the tape Explanation

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c: Left stack represents tape left of head, right stack represents tape at and right of head Explanation

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d: Stacks are used only for temporary storage, not tape simulation Explanation

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In the DTM approach to w#w recognition, what does the marking strategy accomplish?

a: It deletes characters that have been processed Explanation

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b: It marks characters for faster access during comparison Explanation

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c: It enables character-by-character verification between the two parts Explanation

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d: It converts the input to a different alphabet Explanation

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What happens when a 2-stack PDA processes the '#' symbol in the w#w recognition algorithm?

a: It immediately accepts the string Explanation

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b: It switches from storing mode to comparison mode Explanation

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c: It empties both stacks to start fresh Explanation

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d: It duplicates the left stack contents to the right stack Explanation

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What is the significance of the equivalence between 2-stack PDAs and Deterministic Turing Machines?

a: It proves that all computational models are identical Explanation

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b: It shows that multiple memory organizations can achieve universal computation Explanation

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c: It demonstrates that stack-based models are superior to tape-based models Explanation

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d: It establishes that deterministic computation is more powerful than nondeterministic Explanation

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Why might the simulation of a DTM by a 2-stack PDA involve computational overhead?

a: Stack operations are inherently slower than tape operations Explanation

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b: The simulation requires converting between different memory access patterns Explanation

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c: 2-stack PDAs cannot directly implement all DTM operations Explanation

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d: The equivalence is only theoretical, not practical Explanation

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How does understanding 2-PDA and DTM equivalence inform practical algorithm design?

a: It suggests that all algorithms should use stack-based implementations Explanation

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b: It proves that tape-based approaches are always more efficient Explanation

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c: It provides insight into choosing appropriate memory models based on problem structure Explanation

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d: It shows that computational model choice has no practical impact Explanation

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