The idea of impossible fingerings is ambiguous - I can play that D minor voicing in that position as 2 - 4 - 4 - 3. It'd be interesting to see if you could take a set of samples from the user first and apply that to your algorithm. Also useful would be something that purely takes a set of pitches as input, and produces fingerings with the same pitches across various fretted\open strings (and possibly allowing for octave transposition).