Abstract
It is proved that there exists, for every set B ε NP − co-NP, a set A ∋ NP ⌣ co-NP such that A and B have the same deterministic time complexity. Note that B is easier, nondeterministically, than both A and AĀ in that B ε NP while A ∋ NP ⌣ co-NP. We also prove there exists, for each B ∋ NP − co-NP, a set A ∋ NP ⌣ co-NP such that the deterministic time complexity of A is less than that of B on some infinite set. In this case then, A is easier than B deterministically while B is easier than A nondeterministically.
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