Simplicial Complexes and Boolean functions

 

Title: Simplicial Complexes and Boolean functions
Authors: Jesús Aransay, Alejandro del Campo (alejandro /dot/ del-campo /at/ alum /dot/ unirioja /dot/ es) and Julius Michaelis
Submission date: 2021-11-29
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.
BibTeX:
@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   = nov,
  year    = 2021,
  note    = {\url{https://isa-afp.org/entries/Simplicial_complexes_and_boolean_functions.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Jordan_Normal_Form, ROBDD