Additional Details Required To Visualize or Implement Turing Machines
In the words of van Emde Boas (1990), p. 6: "The set-theoretical object provides only partial information on how the machine will behave and what its computations will look like."
For instance,
- There will need to be many decisions on what the symbols actually look like, and a failproof way of reading and writing symbols indefinitely.
- The shift left and shift right operations may shift the tape head across the tape, but when actually building a Turing machine it is more practical to make the tape slide back and forth under the head instead.
- The tape can be finite, and automatically extended with blanks as needed (which is closest to the mathematical definition), but it is more common to think of it as stretching infinitely at both ends and being pre-filled with blanks except on the explicitly given finite fragment the tape head is on. (This is, of course, not implementable in practice.) The tape cannot be fixed in length, since that would not correspond to the given definition and would seriously limit the range of computations the machine can perform to those of a linear bounded automaton.
Read more about this topic: Turing Machine
Famous quotes containing the words additional, details, required, visualize and/or machines:
“Dog. A kind of additional or subsidiary Deity designed to catch the overflow and surplus of the world’s worship.”
—Ambrose Bierce (1842–1914)
“Working women today are trying to achieve in the work world what men have achieved all along—but men have always had the help of a woman at home who took care of all the other details of living! Today the working woman is also that woman at home, and without support services in the workplace and a respect for the work women do within and outside the home, the attempt to do both is taking its toll—on women, on men, and on our children.”
—Jeanne Elium (20th century)
“She, as a veil down to the slender waist,
Her unadorned golden tresses wore
Dishevelled, but in wanton ringlets waved
As the vine curls her tendrils, which implied
Subjection, but required with gentle sway,
And by her yielded, by him best received,
Yielded with coy submission, modest pride,
And sweet, reluctant, amorous delay.
Nor those mysterious parts were then concealed:
Then was not guilty shame: dishonest Shame
Of Nature’s works, Honour dishonourable.”
—John Milton (1608–1674)
“... a family I know ... bought an acre in the country on which to build a house. For many years, while they lacked the money to build, they visited the site regularly and picnicked on a knoll, the site’s most attractive feature. They liked so much to visualize themselves as always there, that when they finally built they put the house on the knoll. But then the knoll was gone. Somehow they had not realized they would destroy it and lose it by supplanting it with themselves.”
—Jane Jacobs (b. 1916)
“The machines that are first invented to perform any particular movement are always the most complex, and succeeding artists generally discover that, with fewer wheels, with fewer principles of motion, than had originally been employed, the same effects may be more easily produced. The first systems, in the same manner, are always the most complex.”
—Adam Smith (1723–1790)