Computer Science MCQs (Set–29 | Level — Frontier Open Conjectures & Deep Structural Theory ๐Ÿ˜ˆ๐Ÿ”ฅ)

281. The statement “P ≠ NP” would immediately imply: A) NP ⊄ P B) No NP-Complete problem is solvable in polynomial time C) There exist problems verifiable but not efficiently solvable D) All of the above Answer: D) All of the above 282. The class coNP consists of languages whose complements are in: A) P B) NP C) PSPACE D) EXP Answer: B) NP 283. If PH collapses to level k, then: A) All higher levels equal ฮฃโ‚–^P B) PSPACE collapses C) NP = PSPACE D) EXP collapses Answer: A) All higher levels equal ฮฃโ‚–^P 284. The problem of graph isomorphism is currently known to be in: A) P (proven decades ago) B) NP-Complete C) Quasi-polynomial time D) PSPACE-Complete Answer: C) Quasi-polynomial time 285. The class #P deals with: A) Optimization problems B) Counting accepting paths C) Space-bounded computation D) Quantum proofs Answer: B) Counting accepting paths 286. If #P = FP (polynomial-time computable functions), then: A) P = NP B) PH collapses C) PSPACE = NP D) BQP = P Answer: B) PH collapses ...
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Computer Science MCQs (Set–25 | 500-Level Research-Oriented Complexity ๐Ÿ˜ˆ๐Ÿ”ฅ)

241. If coNP ⊆ NP, then which major collapse follows?

A) P = NP
B) PH collapses to NP
C) PSPACE = NP
D) EXPTIME = NP

Answer: B) PH collapses to NP

242. The language TRUE quantified Boolean formulas with k alternations is complete for:

A) NP
B) coNP
C) ฮฃโ‚–^P
D) PSPACE

Answer: C) ฮฃโ‚–^P

243. Ladner’s Theorem states that if P ≠ NP, then:

A) NP-Complete problems do not exist
B) There exist NP-intermediate problems
C) PH collapses
D) PSPACE = NP

Answer: B) There exist NP-intermediate problems

244. The class IP (Interactive Polynomial time) is equal to:

A) NP
B) coNP
C) PSPACE
D) EXPTIME

Answer: C) PSPACE

245. Which of the following is known about NL and coNL?

A) NL ≠ coNL
B) NL ⊆ coNL
C) NL = coNL
D) Unknown

Answer: C) NL = coNL

246. If NP = P, then which of the following becomes true?

A) Every language in NP has polynomial-size circuits
B) PH collapses to P
C) NP = coNP
D) All of the above

Answer: D) All of the above

247. The problem of determining whether a Turing Machine accepts infinitely many strings is:

A) Decidable
B) Undecidable
C) NP-Complete
D) PSPACE-Complete

Answer: B) Undecidable

248. Which of the following is complete for EXPTIME?

A) Generalized Chess
B) 3-SAT
C) Graph Coloring
D) QBF

Answer: A) Generalized Chess

249. The circuit minimization problem is:

A) Known NP-Complete
B) Known in P
C) Believed hard, exact complexity unknown
D) PSPACE-Complete

Answer: C) Believed hard, exact complexity unknown

250. MIP (Multi-prover Interactive Proofs) is equal to:

A) NP
B) PSPACE
C) NEXP
D) EXPTIME

Answer: C) NEXP

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