Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity II: A Simple Example
Abstract
In a previous paper we have suggested a number of ideas to attack circuit size complexity with cohomology. As a simple example, we take circuits that can only compute the AND of two inputs, which essentially reduces to SET COVER. We show a very special case of the cohomological approach (one particular free category, using injective and superskyscraper sheaves) gives the linear programming bound coming from the relaxation of the standard integer programming reformulation of SET COVER.
 Publication:

arXiv eprints
 Pub Date:
 April 2006
 arXiv:
 arXiv:cs/0604024
 Bibcode:
 2006cs........4024F
 Keywords:

 Computer Science  Computational Complexity;
 Mathematics  Algebraic Geometry
 EPrint:
 8 pages