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Description numbers are numbers that arise in the theory of Turing machines. They are very similar to Gödel numbers, and are also occasionally called "Gödel numbers" in the literature. Given some universal Turing machine, every Turing machine can, given its encoding on that machine, be assigned a number. This is the machine's description number.
Turing's a-machine model. Turing's a-machine (as he called it) was left-ended, right-end-infinite. He provided symbols əə to mark the left end. A finite number of tape symbols were permitted. The instructions (if a universal machine), and the "input" and "out" were written only on "F-squares", and markers were to appear on "E-squares".
Little Man Computer simulator. The Little Man Computer (LMC) is an instructional model of a computer, created by Dr. Stuart Madnick in 1965. [1] The LMC is generally used to teach students, because it models a simple von Neumann architecture computer—which has all of the basic features of a modern computer.
With regard to what actions the machine actually does, Turing (1936) [2] states the following: "This [example] table (and all succeeding tables of the same kind) is to be understood to mean that for a configuration described in the first two columns the operations in the third column are carried out successively, and the machine then goes over into the m-configuration in the final column."
Roger Penrose provides examples of ways to encode instructions for the Universal machine using only binary symbols { 0, 1 }, or { blank, mark | }. Penrose goes further and writes out his entire U-machine code. He asserts that it truly is a U-machine code, an enormous number that spans almost 2 full pages of 1's and 0's. [19]
A number of other uncomputable functions can also be defined based on measuring the performance of Turing machines in other ways than time or maximal number of ones. [9] For example: [9] The function () is defined to be the maximum number of contiguous ones a halting Turing machine can write on a blank tape.
Besides using Gödel numbering to encode unique sequences of symbols into unique natural numbers (i.e. place numbers into mutually exclusive or one-to-one correspondence with the sequences), we can use it to encode whole “architectures” of sophisticated “machines”. For example, we can encode Markov algorithms, [3] or Turing machines [4 ...
A recreation of MENACE built in 2015. The Matchbox Educable Noughts and Crosses Engine (sometimes called the Machine Educable Noughts and Crosses Engine or MENACE) was a mechanical computer made from 304 matchboxes designed and built by artificial intelligence researcher Donald Michie in 1961.