The inverse behavior of a reversible one-dimensional cellular automaton obtained by a single welch diagram

Mora, Juan C.S.T; Martinez, Genaro J.; McIntosh, Harold V.

Abstract

Reversible cellular automata are discrete dynamical systems based on local interactions which are able to produce an invertible global behavior. Reversible automata have been carefully analyzed by means of graph and matrix tools, in particular the extensions of the ancestors in these systems have a complete representation by Welch diagrams. This paper illustrates how the whole information of a reversible one-dimensional cellular automaton is conserved at both sides of the ancestors for sequences with an adequate length. We give this result implementing a procedure to obtain the inverse behavior by means of calculating and studying a single Welch diagram corresponding with the extensions of only one side of the ancestors. This work is a continuation of our study about reversible automata both in the local and global sense. An illustrative example is also presented.

Citation

Mora, J. C., Martinez, G. J., & McIntosh, H. V. (2006). The inverse behavior of a reversible one-dimensional cellular automaton obtained by a single welch diagram. Journal of Cellular Automata, 1(1), 25-39

• Journal Article Type: Article
• Publication Date: Jan 1, 2006
• Deposit Date: Jul 26, 2010
• Publicly Available Date: Dec 2, 2016
• Journal: Journal of Cellular Automata
• Print ISSN: 1557-5969
• Publisher: Old City Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 1
• Issue: 1
• Pages: 25-39
• Keywords: cellular automaton
• Public URL: https://uwe-repository.worktribe.com/output/1044770
• Publisher URL: http://www.oldcitypublishing.com/JCA/JCAcontents/JCAv1n1contents.html