CA PREDECESSOR

Input: A one-dimensional cellular automaton f (finite state) and a state "a"

Output: Is there a state a' such that a = f (a)?

Please show the algorithm (statement or pseudo) using dynamic programming. Thank you!

Example:

Configuration (f): 111 110 101 100 011 010 001 000

0 0 0 1 1 1 1 0

a = 0 1 0 0 1 1

a' = 1 0 1 1 1 0 0 1 = f(a)