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Contents of README follows

This is an experiment into genetic algorithms on Turing machines. We use the GNU Multi-Precision arithmetic library (GMP) to store our tapes as arbitrarily large integers, and use bit fiddling to implement the Turing Machine’s read and write.

These Turing machines are adapted from Turlough Neary’s “Small universal Turing Machines”, and use a binary alphabet. This keeps the logic simple, at the expense of a large number of states (15 in the standard case, 17 in the monotone machine).

turing.c: This is a simple Turing Machine simulation. It contains a machine with a single tape and a single head.

monotone.c: This implements a “monotone” Turing Machine. Such a machine has three tapes: an input tape, and output tape and a work tape. The work tape behaves like a standard Turing Machine, whilst the input and output tapes can only be moved one way. This ensures that input is never duplicated, and output is never overwritten.

The transitions in a monotone Turing Machine can depend on the symbols under all three heads, but in this case we simply replace the halting state of Neary’s machine with a simple branch to handle input and output. The tape contents (0 or 1) determine whether we read or write. If we read, the contents of the current input cell are written to the left of the work cell that told us to read. We then enter state 0. If we are writing to the output then we enter a new state, and then write the current work tape cell (0 or 1) to the output. Again we move left and enter state 0.

Monotone machines are interesting because they a) do not halt and b) have a definite output.

  1. is useful because, for our purposes, we do not care about machines that halt. This reduces the fraction of useless machines that we will encounter.
  2. is useful because, for our purposes (investigating Kolmogorov complexity), we would like to know when to stop a machine that’s not working. When we haven’t got enough output yet, there’s no way to know if we ever will (eg. we need a timeout), but once enough bits are written, we can stop the simulation.