Models Equivalent To The Turing Machine Model
See also: Turing machine equivalents, Register machine, and Post–Turing machineMany 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:
“French rhetorical models are too narrow for the English tradition. Most pernicious of French imports is the notion that there is no person behind a text. Is there anything more affected, aggressive, and relentlessly concrete than a Parisan intellectual behind his/her turgid text? The Parisian is a provincial when he pretends to speak for the universe.”
—Camille Paglia (b. 1947)
“Perhaps basketball and poetry have just a few things in common, but the most important is the possibility of transcendence. The opposite is labor. In writing, every writer knows when he or she is laboring to achieve an effect. You want to get from here to there, but find yourself willing it, forcing it. The equivalent in basketball is aiming your shot, a kind of strained and usually ineffective purposefulness. What you want is to be in some kind of flow, each next moment a discovery.”
—Stephen Dunn (b. 1939)
“The momentary charge at Balaklava, in obedience to a blundering command, proving what a perfect machine the soldier is, has, properly enough, been celebrated by a poet laureate; but the steady, and for the most part successful, charge of this man, for some years, against the legions of Slavery, in obedience to an infinitely higher command, is as much more memorable than that as an intelligent and conscientious man is superior to a machine. Do you think that that will go unsung?”
—Henry David Thoreau (18171862)
“One of the most important things we adults can do for young children is to model the kind of person we would like them to be.”
—Carol B. Hillman (20th century)