Predecessor states for certain cellular automata evolutions (Q1101228)

This paper reports the solution of the problem of finding which inputs for a function of discrete variables will result in any specified output for the set of binomially determined nearest neighbor additive cellular automata defined on finite or half-infinite sequences. In computing the solution to this problem a process which is the discrete analog to backward integration is defined. This process is determined in terms of an operator which exhibits an interesting period multiplying property.