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SIGACT News Complexity Theory Column 64 Lane A. Hemaspaandra

Summary: SIGACT News Complexity Theory Column 64
Lane A. Hemaspaandra
Dept. of Computer Science, University of Rochester
Rochester, NY 14627, USA
Introduction to Complexity Theory Column 64
Warmest thanks to Christian Glaßer, Mitsunori Ogihara, Aduri Pavan, Alan L. Selman, and Liyu
Zhang for this issue's column. I find the advances they are describing inspiring. These authors
had the courage to approach fundamental, long-standing open issues on what properties many-one
complete sets for crucial classes, such as NP, possess, and these authors quite beautifully resolved
those issues. In particular, their work shows that for a wide range of central complexity classes
(including NP), the nontrivial many-one complete sets are always many-one autoreducible, and
their work also (combined with earlier work of Ambos-Spies) shows that for nontrivial sets, being
many-one mitotic (basically, being a set that some P set can slice into two parts, each of which
is equivalent to the other and to the original set) and being many-one autoreducible coincide.
These are two separate advances, each impressive, and in their wake, the field now knows that all
nontrivial NP-complete sets are many-one autoreducible and many-one mitotic. The work of these
authors, and others, has established a broad range of insights into what redundancy properties
complete sets inherently posses, and this article presents that exciting stream of work. Enjoy!
Please stay tuned to future issues for what I suspect is going to be a particularly exciting
set of articles in this column (note: in all cases the topics/titles are tentative): Zeev Dvir (on


Source: Aduri, Pavan - Department of Computer Science, Iowa State University


Collections: Computer Technologies and Information Sciences