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Complexity classes and number of problems

I know that almost all of complexity classes that have some significance have infinite number of decision problems.

Then what about complete area of these complexity classes? I know that the concept of complete is somewhat artificial, as it depends on some reduction processes.

So, for example, will NP-complete contain infinite number of problems?

Thanks.

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user2346
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    There are certainly infinitely many NP-complete problems; for example, determining whether a graph is $k$-colorable is NP-complete for any $k \geq 3$. I suspect that you could come up with similarly trivial examples for just about any complexity class... – Micah May 20 '12 at 04:32

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The class of $\mathcal{NP}$-complete problems is infinite, as are all the complexity classes that are interesting, because for any finite "complexity class" $\mathcal C$, there is an algorithm to solve problems from $\mathcal C$ in constant time.

MJD
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