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)
“Different persons growing up in the same language are like different bushes trimmed and trained to take the shape of identical elephants. The anatomical details of twigs and branches will fulfill the elephantine form differently from bush to bush, but the overall outward results are alike.”
—Willard Van Orman Quine (b. 1908)
“There were some schools, so called [in my youth]; but no qualification was ever required of a teacher, beyond “readin, writin, and cipherin,” to the Rule of Three. If a straggler supposed to understand latin, happened to sojourn in the neighborhood, he was looked upon as a wizzard. There was absolutely nothing to excite ambition for education.”
—Abraham Lincoln (1809–1865)
“Dear friend,
please do not think
that I visualize guitars playing
or my father arching his bone.
I do not even expect my mother’s mouth.
I know that I have died before....”
—Anne Sexton (1928–1974)
“Shoes are the first adult machines we are given to master.”
—Nicholson Baker (b. 1957)