Virtual Labs

Acceptance by Non-Deterministic Turing Machines

The exploration of multiple paths in a non-deterministic Turing machine (NDTM) is significant because it:

a: Guarantees a solution to NP problems Explanation

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b: Demonstrates a (theoretical) way to solve problems that may not be efficiently solvable by deterministic machines Explanation

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c: Makes NDTMs faster than deterministic machines Explanation

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d: Allows NDTMs to solve problems outside of NP Explanation

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A deterministic Turing machine is characterized by:

a: Exploring multiple computational paths simultaneously Explanation

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b: Making random decisions at each step Explanation

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c: Following a single, defined computational path for a given input Explanation

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d: Solving problems that non-deterministic machines cannot Explanation

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Which statement is true about regular languages?

a: They can only be recognized by non-deterministic machines Explanation

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b: They are more complex than context-free languages Explanation

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c: They are recognized by both deterministic and non-deterministic finite automata Explanation

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d: They require Turing machines (or higher) for recognition Explanation

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What does it mean for a problem to be NP-hard?

a: It can be solved in polynomial time Explanation

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b: Its solution can be verified in polynomial time Explanation

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c: It is at least as hard as the hardest problems in NP Explanation

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d: It is solvable by non-deterministic machines only Explanation

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In computational theory, 'NP' refers to problems where:

a: Solutions can be found in non-polynomial time Explanation

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b: Solutions can be verified in polynomial time by a DTM Explanation

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c: Deterministic machines can find solutions faster than non-deterministic machines Explanation

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d: Solutions are always available but hard to compute Explanation

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How does an NDTM 'solve' the Traveling Salesman Problem in polynomial time?

a: By using a more efficient algorithm than DTM Explanation

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b: By exploring all possible tours simultaneously and selecting the shortest one Explanation

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c: By using heuristics to approximate the solution Explanation

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d: By reducing the problem to a simpler one Explanation

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What is the key insight behind the equivalence of 'NDTM solvable in polynomial time' and 'DTM verifiable in polynomial time'?

a: Both require the same amount of memory Explanation

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b: If an NDTM can find a solution quickly, a DTM can verify that solution quickly Explanation

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c: Both use the same algorithms Explanation

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d: Both have the same time complexity Explanation

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Why is the optimization version of TSP considered NP-Hard rather than just NP?

a: It requires exponential time to solve Explanation

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b: It asks for the best solution, not just a yes/no answer Explanation

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c: It cannot be verified in polynomial time Explanation

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d: It is undecidable Explanation

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What does it mean for a problem to be NP-Complete?

a: It is both in NP and NP-Hard Explanation

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b: It can be solved in polynomial time Explanation

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c: It is the hardest problem in computer science Explanation

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d: It cannot be solved by any algorithm Explanation

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In the context of Sudoku as an NP problem, what can be verified in polynomial time?

a: Whether a puzzle has a unique solution Explanation

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b: Whether a completed grid satisfies all Sudoku constraints Explanation

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c: The minimum number of clues needed for a valid puzzle Explanation

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d: Whether a puzzle is the hardest possible Explanation

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What is the main theoretical advantage of NDTMs over DTMs?

a: They can solve undecidable problems Explanation

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b: They can potentially solve certain problems faster Explanation

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c: They use less memory Explanation

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d: They are easier to program Explanation

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How does the 'librarian analogy' help explain NDTM operation?

a: The librarian can read multiple books simultaneously Explanation

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b: The librarian can clone themselves to explore different paths Explanation

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c: The librarian has perfect memory of all books Explanation

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d: The librarian can rearrange the entire library instantly Explanation

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What is the relationship between NP and co-NP?

a: They are the same class Explanation

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b: co-NP contains the complements of NP problems Explanation

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c: co-NP is harder than NP Explanation

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d: co-NP problems cannot be verified Explanation

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Why can't NDTMs be physically implemented?

a: They require infinite memory Explanation

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b: They need to explore exponentially many paths simultaneously Explanation

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c: They violate the laws of physics Explanation

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d: They require quantum computers Explanation

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What is the difference between NDTMs and Probabilistic Turing Machines (PTMs)?

a: NDTMs are faster than PTMs Explanation

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b: NDTMs explore all paths while PTMs choose paths probabilistically Explanation

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c: PTMs can solve harder problems than NDTMs Explanation

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d: There is no difference Explanation

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In practice, how do we simulate NDTM computation?

a: By using quantum computers Explanation

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b: By using parallel processing Explanation

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c: By systematically exploring all possible computation paths using backtracking Explanation

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d: By using approximation algorithms Explanation

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What would be the implications if P = NP were proven true?

a: All problems would become solvable Explanation

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b: Cryptography would become impossible Explanation

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c: Many currently difficult problems would have efficient solutions Explanation

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d: Computers would become infinitely fast Explanation

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