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 [15] and global [16] sense. An illustrative example is also presented.
