SIAM Journal on Computing


SIAM J. Comput., 31(2), 496–526. (31 pages)

Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems

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Article Data

History

Published online: 27 July 2006

AMS Subject Headings

20G05, 03D15, 70G55

Publication Data

ISSN (print): 0097-5397
ISSN (online): 1095-7111
Publisher: Society for Industrial and Applied Mathematics
CODEN: smjcat
Ketan D. Mulmuley and Milind Sohoni
DOI:10.1137/S009753970038715X

We suggest an approach based on geometric invariant theory to the fundamental lower bound problems in complexity theory concerning formula and circuit size. Specifically, we introduce the notion of a partially stable point in a reductive-group representation, which generalizes the notion of stability in geometric invariant theory due to Mumford [Geometric Invariant Theory, Springer-Verlag, Berlin, 1965]. Then we reduce fundamental lower bound problems in complexity theory to problems concerning infinitesimal neighborhoods of the orbits of partially stable points. We also suggest an approach to tackle the latter class of problems via construction of explicit obstructions.

Copyright © 2001 Society for Industrial and Applied Mathematics
Permalink: http://dx.doi.org/10.1137/S009753970038715X

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