论文信息 - A Certified Module to Study Digital Images with the Kenzo System

A Certified Module to Study Digital Images with the Kenzo System

Kenzo is a Computer Algebra system devoted to Algebraic Topology, written in the Common Lisp programming language. In this paper, programs which allow us to analyze monochromatic digital images with the Kenzo system are presented. Besides a complete automated proof of the correctness of our programs is provided. The proof is carried out using ACL2, a system for proving properties of programs written in (a subset of) Common Lisp.

Jónathan Heras | Vico Pascual | Julio Rubio

[1] Rafael Ayala,et al. Homotopy in digital spaces , 2003, Discret. Appl. Math..

[2] Francisco-Jesús Martín-Mateos,et al. ACL2 Verification of Simplicial Degeneracy Programs in the Kenzo System , 2009, Calculemus/MKM.

[3] Jay A. Wood. Spinor groups and algebraic coding theory , 1989, J. Comb. Theory, Ser. A.

[4] Panagiotis Manolios,et al. Computer-Aided Reasoning: An Approach , 2011 .

[5] Dana Mackenzie. Topologists and Roboticists Explore an 'Inchoate World' , 2003, Science.

[6] Francisco-Jesús Martín-Mateos,et al. Applying ACL2 to the Formalization of Algebraic Topology: Simplicial Polynomials , 2011, ITP.

[7] Jónathan Heras,et al. Proving with ACL2 the Correctness of Simplicial Sets in the Kenzo System , 2010, LOPSTR.

[8] W. Eric L. Grimson,et al. Topological Correction of Subcortical Segmentation , 2003, MICCAI.

[9] Terry M. Peters,et al. Medical Image Computing and Computer-Assisted Intervention - MICCAI 2003 , 2003, Lecture Notes in Computer Science.

[10] Jesús Aransay,et al. A Mechanized Proof of the Basic Perturbation Lemma , 2008, Journal of Automated Reasoning.

[11] Rocío González-Díaz,et al. C V ] 2 3 M ay 2 01 1 On the Cohomology of 3 D Digital Images , 2013 .

[12] César Domínguez,et al. Effective homology of bicomplexes, formalized in Coq , 2011, Theor. Comput. Sci..