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Turing Machines and Undecidability

GATE CSE 2012 · Q4

MCQ1 markEasy

Time

Assuming P≠NP\text{P} \neq \text{NP}, which of the following is TRUE\textbf{TRUE}?

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Solution

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Official answer: B) NP-complete ∩ P =

Turing Machines and Undecidability

By definition:

  • A language LL is in NP-complete\text{NP-complete} if L∈NPL \in \text{NP} and every problem in NP\text{NP} is polynomial-time reducible to LL.

  • If any NP-complete\text{NP-complete} problem could be solved in polynomial time (i.e., if NP-complete∩P≠∅\text{NP-complete} \cap \text{P} \neq \varnothing), then every problem in NP\text{NP} would be solvable in polynomial time, implying P=NP\text{P} = \text{NP}.

Therefore, under the assumption that P≠NP\text{P} \neq \text{NP}, no NP-complete\text{NP-complete} problem can belong to P\text{P}. Hence:

NP-complete∩P=∅\text{NP-complete} \cap \text{P} = \varnothing

This makes option (B) the correct statement.

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This Turing Machines and Undecidability previous year question is Q4 of the GATE CSE 2012 paper. Find more GATE CSE PYQs on Turing Machines and Undecidability in Theory of Computation, or browse all GATE CSE PYQs.

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Turing Machines and Undecidability in GATE CSE

Turing Machines and Undecidability has 30 GATE CSE PYQs across 20 papers from 2012 to 2026. 13 of them are 1-mark MCQs like this one, and GATE CSE 2012 has 2.

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GateAI solution cardGATE CSE 2012 · Q4 · MCQ

Assuming P ≠ NP, which of the following is TRUE?

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