Σ	is a finite alphabet of symbols,
Q	is a finite set of states,
q0 ∈ Q	is the designated start state,
δ:Q×Σ → Q	is the transition function,
ρ:Q×Σ → [0, 1]	is a real-valued weight, and
α:Q → [0, 1]	is a function mapping each state to a real-valued weight.