The proposed rule of evolution involved two generations of cells: let
represent the state of the 
cell in generation t.
Then if
were the rule of evolution of any ordinary 
automaton, the new
rule
spans two generations, but can be inverted by writing
on account of the algebraic properties of the exclusive or. Any
other invertible function of two variables could have been used in
place of 
; for boolean variables the only other candidate is
exclusive nor ( equivalence).
