Detailed in these two links [link] [link]is the theory underpinning one of the fundamental overlaps between biology and computationalism - the creation of DNA computers.
The pieces are lengthy but they illustrate how the computer science of finite state automata (not to be confused with cellular automata) are being ported into biology. Finite state machines (as they are also known) are simpler Turing machines, but still capable of executing computation. Like the Turing machine - they are concepts, or abstractions, of a notional computing device which exist independent of the material they are instantiated within.
Of most interest is the diagrams which abstract the ‘software’ portion of the system into elements which might be less readily understood as such, like transition molecules and mRNA.
Also of interest, the nomenclature for these entitites - they are variously referred to as ‘computational genes’ or ‘molecular automatons’