Let P r(σ | #) and P r(# | P ≤k (w)) denote the probability (according to some D ∈ PTD k ) that a word begins with σ and ends after observing P ≤k (w).
then Equation 4 can be rewritten in terms of conditional probability as the probability assigned to a word depends not on the observed contiguous sequences as in a Markov model, but on observed subsequences.