  Trajectories of on-off events are the output of many single molecule
experiments. Usually, one describes the underlying mechanism that generates the
trajectory using a kinetic scheme, and by analyzing the trajectory aims at
deducing this scheme. In a previous work [O. Flomenbom, J. Klafter, and A.
Szabo, submitted (2004)], we showed that when successive events along a
trajectory are uncorrelated, all the information in the trajectory is contained
in two basic functions, which are the waiting time probability functions (PDFs)
of the on state and of the off state. The kinetic schemes that lead to such
uncorrelated trajectories were termed reducible. Here we discuss the reasons
that lead to reducible schemes. In particular, the topology of reducible
schemes is characterized and proven.
