but with machines its easy.
It's not that easy...the Turing machine can't interpret the tape without knowing something about what the 1s and 0's mean. A complied C++ program is gibberish if read through a Perl interpreter.
DNA isn't as abstract as that, anyway. A DNA molecule interacts with other molecules based on its shape, which the sequence of letters defines. There are thousands of molecules in a cell which the DNA strand can interact with, and those molecules are affected by other molecules. Think about it...for the most part, all the DNA in your cells is the same, but obviously the cells in your liver are doing different things than the cells in your skin.
With cells its different we don't really understand the language of
That's not the problem. We just don't understand ALL the relevant interactions, because there are so many of them. There is not one thing reading through the string of DNA once.
I was wandering if there are any particular behaviors of cells that we
can associate to different "outputs" of the DNA tape.
The outputs would be proteins, but you can't just look at the DNA sequence and know what proteins will be made when and in what quantities, not without having empirically learned a lot about those proteins.
Look, there are lots of people who know a lot about computers and a lot about biology. If thinking about DNA as a simple string of information was fruitful, people would be doing that. We don't, because biology is more complicated than that.