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–27 | Level — Cryptography, Derandomization & Circuit Lower Bounds ๐Ÿ˜ˆ๐Ÿ”ฅ)

261. If one-way functions exist, then which class separation follows?

A) P = NP
B) P ≠ UP
C) NP = coNP
D) PSPACE = NP

Answer: B) P ≠ UP

262. The existence of pseudorandom generators implies:

A) P = NP
B) BPP ⊆ P/poly
C) BPP = P (under strong assumptions)
D) NP ⊆ BPP

Answer: C) BPP = P (under strong assumptions)

263. The Nisan–Wigderson framework connects:

A) Quantum computing and NP
B) Circuit lower bounds and derandomization
C) PCP and SAT
D) PSPACE and IP

Answer: B) Circuit lower bounds and derandomization

264. If NP has polynomial-size circuits, then the Polynomial Hierarchy:

A) Is infinite
B) Collapses to ฮฃ₂^P
C) Collapses to P
D) Equals PSPACE

Answer: B) Collapses to ฮฃ₂^P

265. The Karp–Lipton Theorem states that if NP ⊆ P/poly, then:

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

Answer: B) PH collapses

266. The Natural Proofs barrier (by Alexander Razborov and Steven Rudich) shows limitations in proving:

A) P ≠ PSPACE
B) Circuit lower bounds
C) ETH
D) BQP ⊆ PH

Answer: B) Circuit lower bounds

267. The class AM (Arthur–Merlin games) is known to be contained in:

A) NP
B) coNP
C) ฮ ₂^P
D) PSPACE

Answer: D) PSPACE

268. If EXP has polynomial-size circuits, then:

A) EXP = PSPACE
B) EXP = ฮฃ₂^P
C) EXP = MA
D) EXP collapses to P

Answer: B) EXP = ฮฃ₂^P

269. The hardness vs randomness paradigm suggests that strong circuit lower bounds imply:

A) P = NP
B) Derandomization
C) ETH fails
D) Quantum supremacy

Answer: B) Derandomization

270. The statement “NP ⊄ P/poly” would imply:

A) P ≠ NP
B) Strong circuit lower bounds
C) PH is infinite
D) EXP = NEXP

Answer: B) Strong circuit lower bounds

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