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:
“The world will never be long without some good reason to hate the unhappy; their real faults are immediately detected, and if those are not sufficient to sink them into infamy, an additional weight of calumny will be superadded.”
—Samuel Johnson (1709–1784)
“Patience is a most necessary qualification for business; many a man would rather you heard his story than granted his request. One must seem to hear the unreasonable demands of the petulant, unmoved, and the tedious details of the dull, untired. That is the least price that a man must pay for a high station.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“We are often struck by the force and precision of style to which hard-working men, unpracticed in writing, easily attain when required to make the effort. As if plainness and vigor and sincerity, the ornaments of style, were better learned on the farm and in the workshop than in the schools. The sentences written by such rude hands are nervous and tough, like hardened thongs, the sinews of the deer, or the roots of the pine.”
—Henry David Thoreau (1817–1862)
“... 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 machine has had a pernicious effect upon virtue, pity, and love, and young men used to machines which induce inertia, and fear, are near impotents.”
—Edward Dahlberg (1900–1977)