# Category Advanced

# On Rogozhin's Universal Turing Machines

## How to prove that a Turing Machine is Universal

Every now and then, we see some headline about Turing Completeness of *something*. For example, Minecraft or Dwarf Fortress, or even Minesweeper are famous examples of accidentally Turing complete systems.

If you know what a Turing machine is (and you should) you will have an intuitive idea of the claim: you know that *X can compute any computable function*. Sure; but if you stop thinking about that for a bit, it is not so intuitive **how** we can prove that. If we think long enough, we can start understanding how X can simulate a Turing machine, but **how can we be sure that we can encode a Universal Turing Machine** and **what is the program of a UTM and how we can prove that it is, in fact, universal?**