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
The classic Busy Beaver game asks how long an n-state k-color Turing machine program can run before executing a halt instruction. The phrase “executing a halt instruction” is not normally used in stating the problem; instead, people just say “halting”. But executing a halt instruction is just one way for a program to signal that it is finished. From the point of view of a programmer trying to maximize machine steps, it’s about the worst termination signal possible because it require...| 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
🚰 This post is a continuation of “Halt, Quasihalt, Recur”. 🚰| 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