The reversed time dynamics of a second-order automaton may be described by another second-order automaton with the same neighborhood, in which the function mapping neighborhoods to permutations gives the inverse permutation to . That is, on each possible neighborhood , and should be inverse permutations. With this reverse rule, the automaton described by function correctly computes the configuration at time from the configurations at time and . Because every second-order automaton can be reversed in this way, it follows that they are all reversible cellular automata, regardless of which function is chosen to determine the automaton rule.