Talk:205: Candy Button Paper
It is possible to run a Turing machine on a candy belt:
Marvin Minsky (1967), Computation: Finite and Infinite Machines, Prentice-Hall, Inc. Englewood Cliffs, N.J. In particular see p. 262ff (italics in original): "We can now demonstrate the remarkable fact, first shown by Wang , that for any Turing machine T there is an equivalent Turing machine TN that never changes a once-written symbol! In fact, we will construct a two-symbol machine TN that can only change blank squares on its tape to 1's but can not change a 1 back to a blank." Minsky then offers a proof of this. -- Kopa Leo 188.8.131.52 16:01, 6 July 2013 (UTC)
- In my opinion, intuitively, when writing is demanded, a turing machine just have to copy those symbols to a new location, minding the symbol that needs to be written. It can have a start-of-data mark so this would be transparent to other operations 184.108.40.206 05:45, 27 July 2014 (UTC)
Candy button paper was around long before 1980. I remember it from the 1950s. 220.127.116.11 17:59, 2 October 2016 (UTC)
Doesn't Randall mention three different strategies? The comic says two, however.
- There are two main strategies (careful and fast) and one very uncommon strategy (Turing). 18.104.22.168 21:14, 3 August 2017 (UTC)
There's a proof from Sipser's Introduction to the Theory of Computation (2nd ed), [exercise 3.10: https://archive.org/stream/IntroductionToTheoryOfComputation/introduction%20to%20theory%20of%20computation_djvu.txt]:
We first simulate an ordinary Turing machine by a write-twice Turing machine. The write-twice machine simulates a single step of the original machine by copying the entire tape over to a fresh portion of the tape to the right-hand side of the currently used portion. The copying procedure operates character by character, marking a character as it is copied. This procedure alters each tape square twice, once to write the character for the first time and again to mark that it has been copied. The position of the original Turing machine’s tape head is marked on the tape. When copying the cells at, or adjacent to, the marked position, the tape contents is updated according to the rules of the original Turing machine.
To carry out the simulation with a write-once machine, operate as before, except that each cell of the previous tape is now represented by two cells. The first of these contains the original machine’s tape symbol and the second is for the mark used in the copying procedure. The input is not presented to the machine in the format with two cells per symbol, so the very first time the tape is copied, the copying marks are put directly over the input symbols. -- Kopa Leo 22.214.171.124 12:03, 17 November 2018 (UTC)