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IPM
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YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 470
School of Mathematics
  Title:   Geometry of cut-complexes and threshold logic
  Author(s):  M. R. Emamy-K
  Status:   Published
  Journal: J. Geom.
  Vol.:  65
  Year:  1999
  Pages:   91-100
  Supported by:  IPM
  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 the n-cube by a hyperplane of Rn. Cut-complexes are geometric presentations for threshold Boolean functions and thus are 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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