De Bruijn Graphs and Linear Cellular Automata

De Bruijn graphs provide a convenient way to describe configura tions of linear cellular automata (CAs). Using these graphs, we give a simple quadra tic time algorithm to determine whether a linear CA is reversible. Similarly, one can decide in quadratic time whether the global map of the auto mato n is surjective. We also show that every recursive configuration that has a predecessor on a linear CA already has a recursive predecessor. By contradistinction, it is in general impossible to comput e such a predecessor effectively.