Manindra Agrawal, Eric Allender

We show that all sets complete for NC$^1$ under AC$^0$

reductions are isomorphic under AC$^0$-computable isomorphisms.

Although our proof does not generalize directly to other

complexity classes, we do show that, for all complexity classes C

closed under NC$^1$-computable many-one reductions, the sets ...
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Jochen Me\3ner, Jacobo Toran

A polynomial time computable function $h:\Sigma^*\to\Sigma^*$ whose range

is the set of tautologies in Propositional Logic (TAUT), is called

a proof system. Cook and Reckhow defined this concept

and in order to compare the relative strenth of different proof systems,

they considered the notion ...
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Eric Allender, Harry Buhrman, Michal Koucky, Detlef Ronneburger, Dieter van Melkebeek

We consider sets of strings with high Kolmogorov complexity, mainly

in resource-bounded settings but also in the traditional

recursion-theoretic sense. We present efficient reductions, showing

that these sets are hard and complete for various complexity classes.

In particular, in addition to the usual Kolmogorov complexity measure

K, ...
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Christian Glaßer, Maximilian Witek

We study the autoreducibility and mitoticity of complete sets for NP and other complexity classes, where the main focus is on logspace reducibilities. In particular, we obtain:

- For NP and all other classes of the PH: each logspace many-one-complete set is logspace Turing-autoreducible.

- For P, the delta-levels of ...
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