A geometric connection to threshold logic via cubical lattices

A geometric connection to threshold logic via cubical lattices

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Article ID: iaor20117906
Volume: 188
Issue: 1
Start Page Number: 141
End Page Number: 153
Publication Date: Aug 2011
Journal: Annals of Operations Research
Authors:
Keywords: computational geometry, geometric modelling
Abstract:

A cut‐complex is a cubical complex whose vertices are strictly separable from the rest of the vertices of the n‐cube by a hyperplane of R n . These objects render geometric presentations for threshold Boolean functions, the core objects of study in threshold logic. By applying cubical lattices and geometry of rotating hyperplanes, we prove necessary and sufficient conditions to recognize the cut‐complexes with 2 or 3 maximal faces. This result confirms a positive answer to an old conjecture of Metropolis‐Rota concerning cubical lattices.

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