Editing Turing machine (section)

===The "state"===
The word "state" used in context of Turing machines can be a source of confusion, as it can mean two things. Most commentators after Turing have used "state" to mean the name/designator of the current instruction to be performed—i.e. the contents of the state register. But Turing (1936) made a strong distinction between a record of what he called the machine's "m-configuration", and the machine's (or person's) "state of progress" through the computation—the current state of the total system. What Turing called "the state formula" includes both the current instruction and ''all'' the symbols on the tape:

{{blockquote|Thus the state of progress of the computation at any stage is completely determined by the note of instructions and the symbols on the tape. That is, the ''state of the system'' may be described by a single expression (sequence of symbols) consisting of the symbols on the tape followed by Δ (which is supposed to not to appear elsewhere) and then by the note of instructions. This expression is called the "state formula".|''The Undecidable'', pp. 139–140, emphasis added}}

Earlier in his paper Turing carried this even further: he gives an example where he placed a symbol of the current "m-configuration"—the instruction's label—beneath the scanned square, together with all the symbols on the tape (''The Undecidable'', p.&nbsp;121); this he calls "the ''complete configuration''" (''The Undecidable'', p.&nbsp;118). To print the "complete configuration" on one line, he places the state-label/m-configuration to the ''left'' of the scanned symbol.

A variant of this is seen in Kleene (1952) where [[Stephen Cole Kleene|Kleene]] shows how to write the [[Gödel number]] of a machine's "situation": he places the "m-configuration" symbol q<sub>4</sub> over the scanned square in roughly the center of the 6 non-blank squares on the tape (see the Turing-tape figure in this article) and puts it to the ''right'' of the scanned square. But Kleene refers to "q<sub>4</sub>" itself as "the machine state" (Kleene, p.&nbsp;374–375). Hopcroft and Ullman call this composite the "instantaneous description" and follow the Turing convention of putting the "current state" (instruction-label, m-configuration) to the ''left'' of the scanned symbol (p.&nbsp;149), that is, the instantaneous description is the composite of non-blank symbols to the left, state of the machine, the current symbol scanned by the head, and the non-blank symbols to the right.

''Example: total state of 3-state 2-symbol busy beaver after 3 "moves"'' (taken from example "run" in the figure below):
:: 1'''A'''1
This means: after three moves the tape has ... 000110000 ... on it, the head is scanning the right-most 1, and the state is ''A''. Blanks (in this case represented by "0"s) can be part of the total state as shown here: ''B''01; the tape has a single 1 on it, but the head is scanning the 0 ("blank") to its left and the state is ''B''.

"State" in the context of Turing machines should be clarified as to which is being described:  the current instruction, or the list of symbols on the tape together with the current instruction, or  the list of symbols on the tape together with the current instruction placed to the left of the scanned symbol or to the right of the scanned symbol.

Turing's biographer Andrew Hodges (1983: 107) has noted and discussed this confusion.