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Electronic Colloquium on Computational Complexity

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Reports tagged with complete sets:
TR96-002 | 10th January 1996
Manindra Agrawal, Eric Allender

An Isomorphism Theorem for Circuit Complexity

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 ... more >>>

TR97-026 | 18th June 1997
Jochen Me\3ner, Jacobo Toran

Optimal proof systems for Propositional Logic and complete sets

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 ... more >>>

TR02-028 | 15th May 2002
Eric Allender, Harry Buhrman, Michal Koucky, Detlef Ronneburger, Dieter van Melkebeek

Power from Random Strings

Revisions: 1

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, ... more >>>

TR13-188 | 13th December 2013
Christian Gla├čer, Maximilian Witek

Autoreducibility and Mitoticity of Logspace-Complete Sets for NP and Other Classes

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 ... more >>>

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