Universal Turing Machines II

It's a little easier to see how to build a universal Turing machine if we use a three-tape Turing machine.

One tape holds the "program." This consists of a set of 5-tuples (old state, symbol read, symbol to write, direction, new state).
A second tape holds the current "state" of the Turing machine that we are emulating.
A third tape holds the "input" and will, upon completion, hold the "output." Again, since the tape alphabet of the emulated Turing machine may be larger than the tape alphabet of our universal Turing machine, we may need to encode the alphabet. (This is exactly analogous to using eight bits to represent an ASCII byte.)

We have already noted that a multitape Turing machine is equivalent to a standard Turing machine. In fact, once you get into the details, it's probably easier to do on a single-tape machine.

We will not complete the development of a universal Turing machine, but it isn't as difficult as you might think. One of my textbooks has a complete universal Turing machine in only 23 states (and a reasonably small alphabet).

I have heard of a Turing machine that implements a FORTRAN compiler. Some people have too much time on their hands.