The complexity types of computable sets

The fine structure of time complexity classes for random access machines is analyzed. It is proved that a complexity type C contains sets A,B which are incomparable with respect to polynomial-time reductions if and only if it is not true that C contained in P, and that there is a complexity type C that contains a minimal pair with respect to polynomial-time reductions. The fine structure of P with respect to linear-time reductions is analyzed. It is also shown that every complexity type C contains a sparse set.<
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