From a laymans perspective, can human beings create our own version of DNA, let's say with the use of transistors instead of biological cells, long into the future? Or is DNA just magic and we can't recreate it inside solid state objects like a robot made out of transistors?
DNA sequences are instructions that get printed on the spot and self assemble. This requires a great deal of flexibility so any reproduction would probably look much like what we find in nature.
Or did you understand that and were wondering if we'd ever coopt the bodies mechanisms to create familiar logic gate based compute? Personally I doubt that we'd use already familiar transistors because the process requires ultra pure materials that are modified in very thin layers using gasses to scrape or place individual layers, but maybe we'd find a mechanical analogue expressible via protein, or at that point use purpose built neurons instead.