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

287. The relativization barrier (shown by Theodore Baker, John Gill, and Robert Solovay) shows that:

A) P = NP
B) Oracle results cannot resolve P vs NP
C) NP = PSPACE
D) PH collapses

Answer: B) Oracle results cannot resolve P vs NP

288. The algebrization barrier (by Scott Aaronson and Avi Wigderson) extends limitations of:

A) Circuit complexity
B) Relativization techniques
C) PCP proofs
D) ETH

Answer: B) Relativization techniques

289. The time hierarchy theorem guarantees:

A) P ≠ NP
B) More time gives strictly more power (under certain bounds)
C) PSPACE = NP
D) EXP = NEXP

Answer: B) More time gives strictly more power (under certain bounds)

290. A superpolynomial lower bound for general Boolean circuits computing SAT would imply:

A) ETH fails
B) P = NP
C) NP ⊄ P/poly
D) PH collapses

Answer: C) NP ⊄ P/poly

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