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arXiv:math-ph/0504048math-ph

On Compatibility of Discrete Relations

Vladimir V. Kornyak

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Abstract

An approach to compatibility analysis of systems of discrete relations is proposed. Unlike the Groebner basis technique, the proposed scheme is not based on the polynomial ring structure. It uses more primitive set-theoretic and topological concepts and constructions. We illustrate the approach by application to some two-state cellular automata. In the two-state case the Groebner basis method is also applicable, and we compare both approaches.

arXiv comments
13 pages; to be published in the CASC-2005 proceedings; conclusions added
Journal reference
CASC 2005, LNCS 3718, pp. 272--284, 2005. Springer-Verlag Berlin Heidelberg 2005
DOI
Subjects
math-phMathematical Physics cs.SCSymbolic Computation math.ACCommutative Algebra nlin.CGCellular Automata and Lattice Gases

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  1. Gunnar Carlsson on the Shape of Data (2012) [video] 1 comment

    • Prof Carlsson's (http://math.stanford.edu/~gunnar/) "Topology and Data" paper provides a good overview: http://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01... My recent dive into the literature has enlightened my thinking in terms of database and systems design. It has…

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  2. I Dreamed of a Perfect Database 1 comment

    • Vladimir Kornyak touches on some of these ideas in these papers: 1. On Compatibility of Discrete Relations (2005) http://arxiv.org/pdf/math-ph/0504048.pdf 2. Structural and Symmetry Analysis of Discrete Dynamical Systems (2010) http://arxiv.org/pdf/1006.1754.pdf 3. Discrete…

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