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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."
Descriptions of real machine programs using simpler abstract models are often much more complex than descriptions using Turing machines. For example, a Turing machine describing an algorithm may have a few hundred states, while the equivalent deterministic finite automaton (DFA) on a given real machine has quadrillions.
A simple generalization is the extension to Turing machines with m symbols instead of just 2 (0 and 1). [10] For example a trinary Turing machine with m = 3 symbols would have the symbols 0, 1, and 2. The generalization to Turing machines with n states and m symbols defines the following generalized busy beaver functions:
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.
Smith's proof has unleashed a debate on the precise operational conditions a Turing machine must satisfy in order for it to be candidate universal machine. A universal (2,3) Turing machine has conceivable applications. [19] For instance, a machine that small and simple can be embedded or constructed using a small number of particles or molecules.
A linear bounded automaton is a Turing machine that satisfies the following three conditions: Its input alphabet includes two special symbols, serving as left and right endmarkers. Its transitions may not print other symbols over the endmarkers. Its transitions may neither move to the left of the left endmarker nor to the right of the right ...
Martin Davis makes a persuasive argument that Turing's conception of what is now known as "the stored-program computer", of placing the "action table"—the instructions for the machine—in the same "memory" as the input data, strongly influenced John von Neumann's conception of the first American discrete-symbol (as opposed to analog) computer—the EDVAC.
In fact, Turing's machine does this—it prints on alternate squares, leaving blanks between figures so it can print locator symbols. Turing always left alternate squares blank so his machine could place a symbol to the left of a figure (or a letter if the machine is the universal machine and the scanned square is actually in the “program”).