Computer Science MCQs (Set–31 | Level — Beyond Classical Frontiers ๐Ÿ˜ˆ๐Ÿ”ฅ)

301. The Analytical Hierarchy extends the Arithmetical Hierarchy by allowing quantification over: A) Natural numbers only B) Strings only C) Sets of natural numbers D) Finite automata Answer: C) Sets of natural numbers 302. The problem TOT (set of Turing machines that halt on all inputs) is: A) RE-complete B) coRE-complete C) ฮ ₂⁰-complete D) Decidable Answer: C) ฮ ₂⁰-complete 303. The equality IP = PSPACE was proven by: A) Adi Shamir B) Richard Karp C) Stephen Cook D) John Nash Answer: A) Adi Shamir 304. The PCP Theorem was proven independently by: A) Sanjeev Arora and Shmuel Safra B) Leonid Levin and Michael Rabin C) Andrew Wiles and Terence Tao D) Leslie Valiant and Dana Scott Answer: A) Sanjeev Arora and Shmuel Safra 305. The class AWPP lies between: A) P and NP B) BQP and PP C) PSPACE and EXP D) L and NL Answer: B) BQP and PP 306. The result QIP = PSPACE was shown by: A) Rahul Jain, Zhengfeng Ji, Sarvagya Upadhyay and John Watrous B) Scott Aaronson alone C) Peter Shor D) Noam N...
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Computer Science MCQs (Set–26 | 600-Level Open Problems & Modern Frontiers ๐Ÿ˜ˆ๐Ÿ”ฅ)

251. The famous open problem asking whether every problem whose solution can be verified in polynomial time can also be solved in polynomial time is:

A) NP vs coNP
B) P vs PSPACE
C) P vs NP
D) EXP vs NEXP

Answer: C) P vs NP

252. The Strong Exponential Time Hypothesis (SETH) concerns the time complexity of:

A) Graph Coloring
B) SAT
C) Hamiltonian Cycle
D) Clique

Answer: B) SAT

253. If the Exponential Time Hypothesis (ETH) fails, then:

A) 3-SAT can be solved in sub-exponential time
B) P = NP
C) PSPACE collapses
D) EXPTIME = NP

Answer: A) 3-SAT can be solved in sub-exponential time

254. The Unique Games Conjecture (UGC) has deep implications for:

A) Automata Theory
B) Approximation Hardness
C) Space Complexity
D) Quantum Complexity

Answer: B) Approximation Hardness

255. Which quantum complexity class captures problems solvable by a quantum computer in polynomial time with bounded error?

A) BQP
B) QMA
C) QIP
D) QSPACE

Answer: A) BQP

256. It is known that QIP =

A) NP
B) PSPACE
C) EXP
D) BQP

Answer: B) PSPACE

257. The class QMA is the quantum analogue of:

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

Answer: B) NP

258. The PCP Theorem implies that:

A) P = NP
B) NP has probabilistically checkable proofs
C) NP ⊆ PSPACE
D) SAT is undecidable

Answer: B) NP has probabilistically checkable proofs

259. The class SZK (Statistical Zero Knowledge) is known to be contained in:

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

Answer: C) PSPACE

260. One major unresolved question in quantum complexity theory is whether:

A) BQP ⊆ NP
B) BQP = PSPACE
C) BQP ⊆ PH
D) P = BQP

Answer: C) BQP ⊆ PH

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