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
Turing machine programs are sometimes represented as directed graphs. The vertices of the graph are the program’s states and the edges are transitions between states. The program’s print and shift instructions are relegated to being labels for the edges. Here’s an example:| Something Something Programming