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–23 | 350-Level Ultra Theoretical ๐Ÿ˜ˆ๐Ÿ”ฅ)

221. If EXP = NEXP, which of the following collapses?

A) Polynomial Hierarchy
B) EXPTIME Hierarchy
C) P = NP
D) PSPACE = P

Answer: B) EXPTIME Hierarchy

222. The problem of equivalence of two regular expressions is:

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

Answer: B) PSPACE-Complete

223. If L is NP-Complete and L ≤T P (Turing reduction), then:

A) P = NP
B) L is undecidable
C) NP ⊆ P
D) PSPACE = NP

Answer: C) NP ⊆ P

224. The complement of a context-free language is guaranteed to be:

A) Context-Free
B) Regular
C) Context-Sensitive
D) Recursively Enumerable only

Answer: C) Context-Sensitive

225. In space complexity, PSPACE is closed under:

A) Complement
B) Union
C) Intersection
D) All of the above

Answer: D) All of the above

226. The problem of determining whether a given Turing Machine halts on all inputs is:

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

Answer: C) Undecidable

227. If a Boolean formula has n variables, the total possible truth assignments are:

A) n²
B) 2n
C) 2โฟ
D) n!

Answer: C) 2โฟ

228. In approximation complexity, unless P = NP, which problem has no PTAS?

A) Vertex Cover
B) Knapsack
C) Travelling Salesman Problem (metric)
D) Maximum Clique

Answer: D) Maximum Clique

229. In randomized complexity, RP ⊆ NP because:

A) Deterministic simulation
B) Certificate verification
C) Random guessing
D) Complement closure

Answer: B) Certificate verification

230. The deterministic communication complexity of equality problem (n bits) is:

A) O(1)
B) O(log n)
C) O(n)
D) O(n²)

Answer: C) O(n)

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