The ghost of Turing in his Machine. See the flick! Turing machines are not physical objects but mathematical ones. We require neither soldering irons nor silicon chips to build one. The architecture is simply described, and the actions that may be carried out by the machine are simple and unambiguously specified. Turing recognized that it is not necessary to talk about how the machine carries out its actions, but merely to take as given the twin ideas that the machine can carry out the specified actions, and that those actions may be uniquely described. Turing machines, first described by Alan Turing in (Turing 1937), are simple abstract computational devices intended to help investigate the extent and limitations of what can be computed. Turing was interested in the question of what it means for a task to be computable, which is one of the foundational questions in the philosophy of computer science. Intuitively a task is computable if it is possible to specify a sequence of instructions which will result in the completion of the task when they are carried out by some machine. Such a set of instructions is called an effective procedure, or algorithm, for the task. The problem with this intuition is that what counts as an effective procedure may depend on the capabilities of the machine used to carry out the instructions. In principle, devices with different capabilities may be able to complete different instruction sets, and therefore may result in different classes of computable tasks (see the entry on computability and complexity). Turing proposed a class of devices that came to be known as Turing machines. These devices lead to a formal notion of computation that we will call Turing-computability. A task is Turing computable if it can be carried out by some Turing machine. The proposition that Turings notion captures exactly the intuitive idea of effective procedure is called the Church-Turing thesis. This proposition is not provable, since it is a claim about the relationship between a formal concept and intuition. The thesis would be refuted by an intuitively acceptable algorithm for a task that is not Turing-computable, and no such counterexample has been found. Other independently defined notions of computability based on alternative foundations, such as recursive functions and abacus machines have been shown to be equivalent to Turing-computability. These two facts indicate that there is at least something natural about this notion of computability. Stanford Encyclopedia of Philosophy Turing Machines First published Thu 14 Sep 1995; substantive revision Tue 26 Jun 2012
Posted on: Sat, 22 Nov 2014 06:25:18 +0000
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