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 Busy Beaver question asks how long a Turing machine program of a fixed length can run before halting (or more generally, reaching some particular condition). The question was first posed in 1962. It didn’t take long for researchers to realize that solving this question for any non-trivial case would require the use of computers. Sometimes they named the specific hardware they used. This post is a list of all the computers I have seen mentioned in the literature.| 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
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
🚰 This post is a continuation of “Halt, Quasihalt, Recur”. 🚰| Something Something Programming
The goal of the Busy Beaver contest is to find n-state k-color Turing machine programs that run for as long as possible before halting. It’s basically an optimization problem: what is the longest finite computation that can squeezed out of a program of a certain length? Or from the flip-side: how much description can be packed into a program of a certain length?| Something Something Programming
The Busy Beaver problem asks: among n-state halting Turing machine programs, which one runs the longest? The function BB(n) is famously uncomputable, since calculating it in general would require solving the halting problem. It grows with spectacular speed:| Something Something Programming