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On a Convex Geometric Connection to Threshold Logic

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Combinatorics, Graph Theory and Computing (SEICCGTC 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 448))

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Abstract

A convex geometric connection to Threshold Logic will be reviewed. We have presented necessary and sufficient conditions to recognize cut-complexes with 2 or 3 maximal faces from the class of all cubical complexes. This recognition of cut-complexes is closely related to an old proposal on cubical lattices by N. Metropolis and G. C. Rota. They proposed cubical lattices may also be used for synthesis of Boolean functions parallel to the conventional Boolean algebraic methods. The characterization will be applied to recognize several cut-complexes in the 4-dimensional cube. The cut-complexes of the 4-cube are used to define a new poset that happens to be a distributive lattice.

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Authors and Affiliations

  1. Department of Mathematics, University of Puerto Rico, Box 23355, San Juan, PR, 00931, USA

    M. R. Emamy-K. & Gustavo A. Meléndez Ríos

Authors
  1. M. R. Emamy-K.
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  2. Gustavo A. Meléndez Ríos
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Corresponding author

Correspondence to M. R. Emamy-K. .

Editor information

Editors and Affiliations

  1. Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA

    Frederick Hoffman

  2. Mathematics, Kennesaw State University, Kennesaw, GA, USA

    Sarah Holliday

  3. Mathematics, Florida Atlantic University, Boca Raton, FL, USA

    Zvi Rosen

  4. Computer Science and Engineering, University of North Texas, Denton, TX, USA

    Farhad Shahrokhi

  5. Whiting School of Engineering, Johns Hopkins University, Baltimore, MD, USA

    John Wierman

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Emamy-K., M.R., Meléndez Ríos, G.A. (2024). On a Convex Geometric Connection to Threshold Logic. In: Hoffman, F., Holliday, S., Rosen, Z., Shahrokhi, F., Wierman, J. (eds) Combinatorics, Graph Theory and Computing. SEICCGTC 2021. Springer Proceedings in Mathematics & Statistics, vol 448. Springer, Cham. https://doi.org/10.1007/978-3-031-52969-6_9

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