For any given board state, there are a restricted variety of strikes from a sound earlier state that might have produced what you see now. Provided that, sure, it must be attainable, in precept, to programmatically decide a transfer sequence from a typical beginning board that can produce the state seen.
That stated, there may be the issue of figuring out the validity of the earlier state for every back-move computation — and the extra stones are on the board, the bigger this drawback turns into. I am no sport principle mathematician, and might’t say for sure, but it surely appears very attainable that this prerequisite job is so computationally advanced as to be impractical to find out.
This successfully turns into an issue of ranging from the start state and dealing ahead, possible a Very Massive Quantity of occasions, to find out if a given state is legitimate — which was the issue with brute-force computation of chess and go. Solely when it turned attainable to program software program that performed like a human (ignoring what we’d take into account clearly unhealthy strikes) did the issue turn out to be tractable (together with coaching AI the identical means a human grasp can be skilled, by publicity to a lot of video games).
Like many sport issues, then, whereas in all probability attainable in precept, this will not be sensible with actual world computing with out involving a well-trained AI to validate board states.