User blog:MilkyWay90/The Function with a Programming Language

If anybody has ever programmed in an esoteric/recreational programming language, they know about BrainF***.

Today, I'm going to make a function with that.

\(F(n) = \) the largest possible \(g(n)\) such that \(g(n) = the sum of all the values of each value on the tape generated at the end of a Brain**** progra., assuming it halts with n characters. Otherwise, it is -1.

We are assuming there is no STDIN and that the tape is infinite, and that the maximum/minimum value of the pointer has no bounds (In the interpreter, it has a maximum/minimum of 256/-256, respectively).

F(0) = 0, because the empty program does nothing

F(1) = 1, because of the program

F(2) = 2, because of the program

It may seem like F(n) = n, but it is not, because when you have enough characters to make a loop, then it can do addition, multiplication, \(f_{\omega}(n)\), and more because BrainF*** is a Turing-complete programming language.

I'll try putting in a formal definition later, but this is uncomputable because BrainF*** is a Turing-complete programming language.