Simplicial Complexes and Boolean functions

Jesús Aransay 🌐, Alejandro del Campo 📧 and Julius Michaelis 🌐

November 29, 2021

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

In this work we formalise the isomorphism between simplicial complexes of dimension $n$ and monotone Boolean functions in $n$ variables, mainly following the definitions and results as introduced by N. A. Scoville. We also take advantage of the AFP representation of ROBDD (Reduced Ordered Binary Decision Diagrams) to compute the ROBDD representation of a given simplicial complex (by means of the isomorphism to Boolean functions). Some examples of simplicial complexes and associated Boolean functions are also presented.

License

BSD License

Topics

Session Simplicial_complexes_and_boolean_functions

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× 
@article{Simplicial_complexes_and_boolean_functions-AFP,
  author  = {Jesús Aransay and Alejandro del Campo and Julius Michaelis},
  title   = {Simplicial Complexes and Boolean functions},
  journal = {Archive of Formal Proofs},
  month   = {November},
  year    = {2021},
  note    = {\url{https://isa-afp.org/entries/Simplicial_complexes_and_boolean_functions.html},
             Formal proof development},
  ISSN    = {2150-914x},
}
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