Regular patterns in Coxeter groups


A deterministic automaton is
  • a graph with edges labeled by items from a set of symbols called its alphabet
  • a single node designated the start state
  • a subset of nodes called accepting states
such that every node has at most one edge from it labeled by any symbol. There is also an implicit failure state to which all edges not explicitly mentioned lead.

A possibly non-deterministic one may also have edges labeled by a null symbol, several start states, and several edges with the same source and label.