Quasi global-equivalence in one-dimensional binary cellular automata

Despite their apparent simplicity, one-dimensional binary Cellular Automata (CA) are proved to be universal, and their behavior has not been completely characterized yet. It is well-known that there are only 88 globally-independent CA rules. Here, we formalize the concept of quasi globally-equivalent rules and analyze its implications by using the nonlinear dynamics perspective of CA, which considers CA as a special case of Cellular Nonlinear Networks. Our conclusion is that the set of 88 globally-independent CA rules is redundant, because only 82 rules are quasi globally-independent.