Do the complete areas of various complexity classes have infinitely many problems?

Question

Possible Duplicate:
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.

Answer 1

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.