Article
Using membrane computing for effective homology
Author/s | Díaz Pernil, Daniel
Christinal, Hepzibah A. Gutiérrez Naranjo, Miguel Ángel ![]() ![]() ![]() ![]() ![]() ![]() ![]() Real Jurado, Pedro ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Publication Date | 2012 |
Deposit Date | 2015-12-23 |
Published in |
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Abstract | Effective Homology is an algebraic-topological method based on the computational concept of chain homotopy equivalence on a cell complex. Using this algebraic data structure, Effective Homology gives answers to some important ... Effective Homology is an algebraic-topological method based on the computational concept of chain homotopy equivalence on a cell complex. Using this algebraic data structure, Effective Homology gives answers to some important computability problems in Algebraic Topology. In a discrete context, Effective Homology can be seen as a combinatorial layer given by a forest graph structure spanning every cell of the complex. In this paper, by taking as input a pixel-based 2D binary object, we present a logarithmic-time uniform solution for describing a chain homotopy operator ϕ for its adjacency graph. This solution is based on Membrane Computing techniques applied to the spanning forest problem and it can be easily extended to higher dimensions. |
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