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Let π be a problem that belongs to the class NP. Then which one of the following is TRUE?
  • a)
    There is no polynomial time algorithm for πA
  • b)
    If πA can be solved deterministically in polynomial time, then P = NP
  • c)
    If πA is NP-hard, then it is NP-complete
  • d)
    πA may be undecidable
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
LetπAbe a problem that belongs to the class NP. Then which one of t...
it is given that πA ∈ NP
∴ If πA is NP-hard, and since it is given that πA ∈ NP , this means that πA is NP-complete
∴ choice (c) is correct.
Notice that choice (a) is incorrect since as P ∈ NP, some NP problems are actually P and hence polynomial time algorithm can exist for these.
Choice (b) is incorrect since, If πA can be solved deterministicaily in polynomial time, it does not generate that P=NP, unless of-course it is additionally known that πA is NP-complete.
Choice (d) is incorrect since,
All problems belonging to P or NP have to be decidable.
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LetπAbe a problem that belongs to the class NP. Then which one of t...
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LetπAbe a problem that belongs to the class NP. Then which one of the following is TRUE?a)There is no polynomial time algorithm forπAb)If πA can be solved deterministically in polynomial time, then P = NPc)If πA is NP-hard, then it is NP-completed)πA may be undecidableCorrect answer is option 'C'. Can you explain this answer?
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