In this talk we will consider deterministic finite automata(DFAs) with a singleton as alphabet. These rather restrictive machines have a strong connection with a very specific field of word combinatorics. In particular we will show how the periodicity of the bouncing DVD logo(or a billiard ball) is related to these automata and generate so-called Fibonacci words. These words form an interesting class of automata that indicates that there might be more efficient methods to compute bisimilarity than the method of partition refinement.
 “Hopcroft’s algorithm and cyclic automata” – Castiglione, Restivo & Sciortino (2008)