A Turing Machine is a description of a machine developed by Alan Turing in the 1930s. This model has been the basis on which modern computers have been built.

The memory of this system is an infinitely-long "tape". This tape is broken up into squares, onto each a symbol can be written. For real-world analogues, consider the bytes of a computer's memory stored as ones and zeros, or, more tangibly, the tape of a cassette, which stores patterns created by magnetism. This memory is written and read by a "head," comparable parts exist in both computers and tape recorders. This head component reads what's on the current square of tape and, according to its set of instructions, writes a symbol and moves the head to the left or the right. Combined with a set of instructions, what we would call the computer's program, this machine is capable of performing a wide array of functions, from addition to division to copying data from different parts of memory.

Currently, large language models lack this memory and execution faculty. They do not produce the same results every time when given the same input, and they have a hard time retaining memory. Thus, LLMs and Turing Machines are different devices, best suited to solving different kinds of problems.
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