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## Main Question or Discussion Point

What are complexity classes (P, NP, etc) in terms of pure sets? ZFC, I mean.

- Thread starter Dragonfall
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- #1

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What are complexity classes (P, NP, etc) in terms of pure sets? ZFC, I mean.

- #2

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P = {problem q | there is a polynomial time algorithm for solving q}

NP = {problem q | there is a non-deterministic polynomial time algorithm for solving q}

NP-Hard = {problem q | any problem q' in NP can be reduced to q in polynomial time}

NP-Complete = NP (intersect) NP-Hard

etc.

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- #4

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"problem q" would also have to be a set.I thought they were just sets. Like

P = {problem q | there is a polynomial time algorithm for solving q}

etc.

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Are you asking for the definition of these sets in terms of elementary set theoretic notions? Like somebody said, doing that would be counterproductive. I think the way to bridge the gap from this to more basic notions is via the mechanism of language and machine.

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CRGreathouse

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