FYI, I have merged the entire contents of this article into semiautomaton. At this time, WP has five distinct articles (e.g. transformation semigroup, transition monoid, state transition system, etc.) all talking about exactly the same thing, all using slightly different notations and language. I'm trying to consolidate/uniformize all of these. If there are objections or comments, please leave them at Talk:Semiautomaton