Christian Glaßer, Alan L. Selman, Samik Sengupta

We prove that all of the following assertions are equivalent:

There is a many-one complete disjoint NP-pair;

there is a strongly many-one complete disjoint NP-pair;

there is a Turing complete disjoint NP-pair such that all reductions

are smart reductions;

there is a complete disjoint NP-pair for one-to-one, invertible ...
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Christian Glaßer, Christian Reitwießner, Victor Selivanov

We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results.

1. NP ... more >>>