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–22 | 300-Level Elite Theory + Trick Numerical ๐Ÿ˜ˆ๐Ÿ†๐Ÿ”ฅ)

211. If NP ⊆ co-NP, then which of the following must hold?

A) NP = co-NP
B) P = NP
C) PSPACE = NP
D) EXP = NP

Answer: A) NP = co-NP

212. Ladner’s Theorem implies that if P ≠ NP, then:

A) No problems lie between P and NP-Complete
B) There exist problems in NP that are neither in P nor NP-Complete
C) NP = PSPACE
D) PH collapses

Answer: B) There exist problems in NP that are neither in P nor NP-Complete

213. The problem of determining whether a CFG generates all possible strings over ฮฃ* is:

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

Answer: D) Undecidable

214. If a Turing Machine runs in time O(n), then it uses at most:

A) O(log n) space
B) O(n) space
C) O(n²) space
D) Constant space

Answer: B) O(n) space

215. In circuit complexity, AC⁰ circuits are characterized by:

A) Polynomial depth
B) Constant depth and unbounded fan-in
C) Logarithmic size
D) Deterministic space

Answer: B) Constant depth and unbounded fan-in

216. The class IP (Interactive Polynomial time) is equal to:

A) NP
B) PSPACE
C) EXPTIME
D) P

Answer: B) PSPACE

217. If a graph has adjacency matrix representation, checking whether an edge exists between two vertices takes:

A) O(V)
B) O(E)
C) O(1)
D) O(log V)

Answer: C) O(1)

218. In Kolmogorov complexity, most binary strings of length n have complexity:

A) O(log n)
B) O(1)
C) ฮ˜(n)
D) ฮ˜(√n)

Answer: C) ฮ˜(n)

219. In distributed systems, CAP theorem states that a distributed system can provide at most:

A) 1 property
B) 2 of the 3 properties
C) All 3 properties simultaneously
D) None

Answer: B) 2 of the 3 properties

220. The deterministic time complexity of integer multiplication using FFT-based algorithm is approximately:

A) O(n²)
B) O(n log n)
C) O(n^1.585)
D) O(n³)

Answer: B) O(n log n)

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