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 Nisan

Answer: A) Jain, Ji, Upadhyay and Watrous

307. The Time Hierarchy Theorem requires the time-constructibility of:

A) Any function
B) Superconstant functions
C) The bounding function
D) Only polynomial functions

Answer: C) The bounding function

308. If NP ⊆ SIZE(n^k) for some k, then by Karp–Lipton:

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

Answer: A) PH collapses

309. A language complete for ฮฃ₂^P typically has the form:

A) ∀x ∃y ฯ†(x,y)
B) ∃x ฯ†(x)
C) ∃x ∀y ฯ†(x,y)
D) ฯ†(x)

Answer: C) ∃x ∀y ฯ†(x,y)

310. The set of true first-order arithmetic statements is:

A) Decidable
B) RE
C) coRE
D) Neither RE nor coRE

Answer: D) Neither RE nor coRE

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