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Electronic Colloquium on Computational Complexity

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Reports tagged with Reducibilities:
TR96-066 | 21st November 1996
Pierluigi Crescenzi, Viggo Kann, Riccardo Silvestri, Luca Trevisan

Structure in Approximation Classes

The study of the approximability properties of NP-hard
optimization problems has recently made great advances mainly due
to the results obtained in the field of proof checking. In a
recent breakthrough the APX-completeness of several important
optimization problems is proved, thus reconciling `two distinct
views of ... more >>>

TR98-027 | 15th April 1998
Vikraman Arvind, Jacobo Toran

Sparse sets, approximable sets, and parallel queries to NP

We relate the existence of disjunctive hard sets for NP to
other well studied hypotheses in complexity theory showing
that if an NP-complete set or a coNP-complete set is
polynomial-time disjunctively reducible
to a sparse set then FP$^{\rm NP}_{||}$ = FP$^{\rm NP[log]}$. Using
a similar argument we obtain also that ... more >>>

TR06-090 | 22nd June 2006
Christian Gla├čer, Alan L. Selman, Stephen Travers, Liyu Zhang

Non-Mitotic Sets

<p> We study the question of the existence of non-mitotic sets in NP. We show under various hypotheses that:</p>
<li>1-tt-mitoticity and m-mitoticity differ on NP.</li>
<li>1-tt-reducibility and m-reducibility differ on NP.</li>
<li>There exist non-T-autoreducible sets in NP (by a result from Ambos-Spies, these sets are neither ... more >>>

TR07-071 | 1st August 2007
Jacobo Toran

Reductions to Graph Isomorphism

We show that several reducibility notions coincide when applied to the
Graph Isomorphism (GI) problem. In particular we show that if a set is
many-one logspace reducible to GI, then it is in fact many-one AC^0
reducible to GI. For the case of Turing reducibilities we show that ... more >>>

TR18-011 | 18th January 2018
John Hitchcock, Hadi Shafei

Nonuniform Reductions and NP-Completeness

Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger complexity classes. We study the power of nonuniform reductions for NP-completeness, obtaining both separations and upper bounds for ... more >>>

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