# Tag: recursion

• ## Modular Machines and their equivalence to Turing Machines

Modular machines are a lesser-known class of automata, which act upon $$\mathbb{N}^2$$ and are actually capable of simulating any Turing Machine - a fact which we will prove here.

• ## Counting Derangements

I present an inefficient yet novel way of recursively counting derangements of a set, and generalise this to counting permutations without short cycles.