Abstract
Geometric methods of convex polytopes are applied to demonstrate a new connection between convexity and threshold logic. A cut-complex is a cubical complex whose vertices are strictly separable from rest of the vertices of then-cube by a hyperplane ofR n. Cutcomplexes are geometric presentations for threshold Boolean functions and thus are related to threshold logic. For an old classical theorem of threshold logic a shorter but geometric proof is given. The dimension of the cube hull of a cut-complex is shown to be the same as the maximum degree of the vertices in the complex. A consequence of the latter result indicates that any two isomorphic cut-complexes are isometric.
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This research was partially supported by FIPI-University of Puerto Rico, by Inter American University of Puerto Rico at Bayamon and by IPM, Tehran, Iran.
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Emamy-K., M.R. Geometry of cut-complexes and threshold logic. J Geom 65, 91–100 (1999). https://doi.org/10.1007/BF01228680
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DOI: https://doi.org/10.1007/BF01228680