Turing Machine - Models Equivalent To The Turing Machine Model

Models Equivalent To The Turing Machine Model

See also: Turing machine equivalents, Register machine, and Post–Turing machine

Many machines that might be thought to have more computational capability than a simple universal Turing machine can be shown to have no more power (Hopcroft and Ullman p. 159, cf Minsky (1967)). They might compute faster, perhaps, or use less memory, or their instruction set might be smaller, but they cannot compute more powerfully (i.e. more mathematical functions). (Recall that the Church–Turing thesis hypothesizes this to be true for any kind of machine: that anything that can be "computed" can be computed by some Turing machine.)

A Turing machine is equivalent to a pushdown automaton that has been made more flexible and concise by relaxing the last-in-first-out requirement of its stack.

At the other extreme, some very simple models turn out to be Turing-equivalent, i.e. to have the same computational power as the Turing machine model.

Common equivalent models are the multi-tape Turing machine, multi-track Turing machine, machines with input and output, and the non-deterministic Turing machine (NDTM) as opposed to the deterministic Turing machine (DTM) for which the action table has at most one entry for each combination of symbol and state.

Read-only, right-moving Turing machines are equivalent to NDFAs (as well as DFAs by conversion using the NDFA to DFA conversion algorithm).

For practical and didactical intentions the equivalent register machine can be used as a usual assembly programming language.

Read more about this topic:  Turing Machine

Famous quotes containing the words models, equivalent, machine and/or model:

    “The parents who wish to lead a quiet life I would say: Tell your children that they are very naughty—much naughtier than most children; point to the young people of some acquaintances as models of perfection, and impress your own children with a deep sense of their own inferiority. You carry so many more guns than they do that they cannot fight you. This is called moral influence and it will enable you to bounce them as much as you please.”
    —Samuel Butler (1835–1902)

    “But then people don’t read literature in order to understand; they read it because they want to re-live the feelings and sensations which they found exciting in the past. Art can be a lot of things; but in actual practice, most of it is merely the mental equivalent of alcohol and cantharides.”
    —Aldous Huxley (1894–1963)

    “Much that is natural, to the will must yield.
    Men manufacture both machine and soul,
    And use what they imperfectly control
    To dare a future from the taken routes.”
    —Thom Gunn (b. 1929)

    “Socrates, who was a perfect model in all great qualities, ... hit on a body and face so ugly and so incongruous with the beauty of his soul, he who was so madly in love with beauty.”
    —Michel de Montaigne (1533–1592)