Content deleted Content added
Erel Segal (talk | contribs) |
This is just a change of perception, a different way of saying the same thing. But in this way you just won’t put it on a pedestal. Thank you. Tags: Reverted Visual edit Mobile edit Mobile web edit |
||
Line 5:
{{Automata theory}}
A '''Turing machine''' is a [[mathematical model of computation]] describing an [[abstract machine]]<ref>Minsky 1967:107 "In his 1936 paper, A. M. Turing defined the class of abstract machines that now bear his name. A Turing machine is a finite-state machine associated with a special kind of environment -- its tape -- in which it can store (and later recover) sequences of symbols," also Stone 1972:8 where the word "machine" is in quotation marks.</ref> that manipulates symbols on a strip of tape according to a table of rules.<ref>Stone 1972:8 states "This "machine" is an abstract mathematical model", also cf. Sipser 2006:137ff that describes the "Turing machine model". Rogers 1987 (1967):13 refers to "Turing's characterization", Boolos Burgess and Jeffrey 2002:25 refers to a "specific kind of idealized machine".</ref>
The machine operates on an infinite<ref>Cf. Sipser 2002:137. Also, Rogers 1987 (1967):13 describes "a paper tape of infinite length in both directions". Minsky 1967:118 states "The tape is regarded as infinite in both directions". Boolos Burgess and Jeffrey 2002:25 include the possibility of "there is someone stationed at each end to add extra blank squares as needed".</ref> memory tape divided into [[discrete mathematics|discrete]] cells,<ref>Cf. Rogers 1987 (1967):13. Other authors use the word "square" e.g. Boolos Burgess Jeffrey 2002:35, Minsky 1967:117, Penrose 1989:37.</ref> each of which can hold a single symbol drawn from a [[finite set]] of symbols called the [[Alphabet (formal languages)|alphabet]] of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a [[finite set]] of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right,<ref>Boolos Burgess Jeffry 2002:25 illustrate the machine as moving along the tape. Penrose 1989:36-37 describes himself as "uncomfortable" with an infinite tape observing that it "might be hard to shift!"; he "prefer[s] to think of the tape as representing some external environment through which our finite device can move" and after observing that the " 'movement' is a convenient way of picturing things" and then suggests that "the device receives all its input from this environment. Some variations of the Turing machine model also allow the head to stay in the same position instead of moving or halting.</ref> or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whether to halt is based on a finite table that specifies what to do for each combination of the current state and the symbol that is read. Like a real computer program, it is possible for a Turing machine to go into an [[infinite loop]] which will never halt.
| |||