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–24 | 400-Level Extreme Proof & Reduction ๐Ÿ”ฅ๐Ÿ˜ˆ)

231. If SAT ∈ P, then which of the following collapses immediately?

A) PH collapses to ฮฃ₁^P
B) NP = coNP
C) PSPACE = P
D) EXPTIME = NP

Answer: A) PH collapses to ฮฃ₁^P

232. The problem of determining whether two context-free grammars generate the same language is:

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

Answer: D) Undecidable

233. If NP ⊆ coNP, then:

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

Answer: A) PH collapses

234. Which of the following is complete for PSPACE under polynomial-time reductions?

A) 3-SAT
B) QBF
C) Vertex Cover
D) Clique

Answer: B) QBF

235. The class BPP is known to be contained in:

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

Answer: C) PSPACE

236. Which hierarchy is known to be infinite?

A) Polynomial Hierarchy
B) Arithmetical Hierarchy
C) EXPTIME Hierarchy
D) None proven infinite

Answer: B) Arithmetical Hierarchy

237. The Post Correspondence Problem (PCP) is:

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

Answer: D) Undecidable

238. If L is recursively enumerable and its complement is also recursively enumerable, then L is:

A) Context-Free
B) Decidable
C) Regular
D) PSPACE-Complete

Answer: B) Decidable

239. Which problem remains NP-Complete even when restricted to planar graphs?

A) Hamiltonian Cycle
B) 2-SAT
C) Minimum Spanning Tree
D) Bipartite Matching

Answer: A) Hamiltonian Cycle

240. Savitch’s Theorem implies:

A) NSPACE(s(n)) = SPACE(s(n))
B) NSPACE(s(n)) ⊆ SPACE(s²(n))
C) PSPACE = NP
D) P = NP

Answer: B) NSPACE(s(n)) ⊆ SPACE(s²(n))

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