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–28 | Level — Quantum, Fine-Grained & Meta-Complexity ๐Ÿ˜ˆ๐Ÿ”ฅ)

271. The class MIP* (multi-prover interactive proofs with entanglement) was shown to equal:

A) NEXP
B) PSPACE
C) RE
D) EXP

Answer: C) RE

272. The breakthrough result MIP* = RE was proved by (among others):

A) Scott Aaronson
B) Ran Raz
C) John von Neumann
D) Claude Shannon

Answer: B) Ran Raz

273. The Orthogonal Vectors Conjecture is central in:

A) Classical cryptography
B) Fine-grained complexity
C) Automata minimization
D) Quantum supremacy

Answer: B) Fine-grained complexity

274. The class PP is known to contain:

A) BPP
B) NP
C) PH
D) All of the above

Answer: D) All of the above

275. Toda’s Theorem states that:

A) PH ⊆ P
B) PH ⊆ PSPACE
C) PH ⊆ P^PP
D) PP ⊆ PH

Answer: C) PH ⊆ P^PP

276. The Minimum Circuit Size Problem (MCSP) is important in:

A) Meta-complexity
B) Graph theory
C) Quantum algorithms
D) Formal languages

Answer: A) Meta-complexity

277. It is known that BQP is contained in:

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

Answer: C) PSPACE

278. The Exponential Time Hypothesis (ETH) implies that 3-SAT cannot be solved in:

A) O(2โฟ) time
B) Subexponential time
C) Polynomial time
D) Logarithmic space

Answer: B) Subexponential time

279. The class ⊕P (Parity-P) is related to:

A) Counting mod 2
B) Deterministic logspace
C) Quantum entanglement
D) Automata equivalence

Answer: A) Counting mod 2

280. A major open problem in circuit complexity is proving superpolynomial lower bounds for circuits computing:

A) Regular languages
B) Context-free languages
C) Explicit functions in NP
D) Finite automata

Answer: C) Explicit functions in NP

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