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–21 | 250+ Level Super Advanced ๐Ÿš€๐Ÿ”ฅ)

201. Which of the following is TRUE regarding the Polynomial Hierarchy (PH)?

A) PH collapses if P = NP
B) PH collapses if NP = co-NP
C) PH collapses if ฮฃ₁^P = ฮฃ₂^P
D) All of the above

Answer: D) All of the above

202. Savitch’s Theorem states that:

A) NSPACE(s(n)) ⊆ DSPACE(s(n))
B) NSPACE(s(n)) ⊆ DSPACE(s(n)²)
C) NP = PSPACE
D) PSPACE = EXPTIME

Answer: B) NSPACE(s(n)) ⊆ DSPACE(s(n)²)

203. If L is PSPACE-Complete and L ∈ NP, then:

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

Answer: B) NP = PSPACE

204. The language equivalence problem for DFAs is:

A) NP-Complete
B) PSPACE-Complete
C) Decidable in polynomial time
D) Undecidable

Answer: C) Decidable in polynomial time

205. In approximation algorithms, a PTAS gives:

A) Exact solution
B) Constant factor approximation only
C) (1 + ฮต) approximation for any fixed ฮต > 0
D) Exponential time solution

Answer: C) (1 + ฮต) approximation for any fixed ฮต > 0

206. In information theory, mutual information is:

A) Always negative
B) Always zero
C) Always non-negative
D) Always 1

Answer: C) Always non-negative

207. A problem is NP-Complete if:

A) It is in NP and NP-Hard
B) It is NP-Hard only
C) It is undecidable
D) It is in P

Answer: A) It is in NP and NP-Hard

208. In randomized complexity, BPP is:

A) Deterministic polynomial time
B) Bounded-error probabilistic polynomial time
C) Exponential time
D) Non-deterministic space

Answer: B) Bounded-error probabilistic polynomial time

209. The problem of checking whether a context-free grammar is ambiguous is:

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

Answer: C) Undecidable

210. In communication complexity, the deterministic complexity of set disjointness is:

A) O(1)
B) O(log n)
C) O(n)
D) O(n²)

Answer: C) O(n)

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