Sounds very similar to KolmogoroV Complexity: https://en.wikipedia.org/wiki/Kolmogorov_complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity In this c

Sounds very similar to KolmogoroV Complexity: https://en.wikipedia.org/wiki/Kolmogorov_complexity https://en.wikipedia.org/wiki/Kolmogorov_complexity In this case your starting automata is acting as a program you want to find the smallest one that produces your object as output. It is in general undecidable to know if you found the smallest possible program that produces a given output.