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Using membrane computing for effective homology

 

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Author: 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
Date: 2012
Published in: Applicable Algebra in Engineering, Communication and Computing, 23 (5), 233-249.
Document type: Article
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 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.
Size: 1.213Mb
Format: PDF

URI: http://hdl.handle.net/11441/32179

DOI: http://dx.doi.org/10.1007/s00200-012-0176-6

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