How long can a Turing machine program run when started on the blank tape before the tape becomes blank again? Of course, this will depend on the length of the program – how many states and colors it has. Even given these parameters, it is logically impossible to calculate how long a self-cleaning Turing machine can run. Any values that can be known have to be discovered empirically.| Something Something Programming
SCENARIO: It’s 1950, and a brand new Turing machine, the first of its kind, has been installed at a research facility. Lots of people want to use it, but the machine has just one tape. A program’s execution can be affected in undesirable ways by data left over on the tape from a previous program run, and so as a matter of etiquette the convention is adopted among the machine’s users that the tape is to be wiped clean after each use. Rather than cleaning the tape manually after program e...| Something Something Programming
Suppose someone claims that a particular Turing machine program halts when run on the blank tape. How can this claim be verified? The obvious answer is to run it on the blank tape and see if it halts. But what if the program in fact does not halt? The verifier will be stuck running a non-halting program, waiting forever for a halt that will never come.| Something Something Programming
The aim of the Busy Beaver game is to find the longest running Turing machine program of n states and k colors. Busy Beaver programs could in principle be written by hand, but nobody has ever succeeded in doing so. Instead, these programs are discovered through exhaustive search. This is done by a two-stage process:| Something Something Programming