Markov models hidden in the threat reduction applications

In a dynamical system, there is a rule which maps states x forward in time. At time t, the current state x(t) of the dynamical system provides all the information necessary to calculate future state, and information about past states is redundant. Thus the sequence of states in the dynamical system satisfies the Markov property. In applications, the measured data can be thought of as being a function of states of a dynamical system with y(t)=G(x(t)). The function F that maps states forward in time and the function G that maps states to observations make up a state space model for sequences of observations. If the observation function is not invertible, then knowledge of the measurement y(t) at a single time t is not sufficient to specify the state x(t) uniquely, and one could say that x(t) is hidden. This is the sense of hidden in the term "hidden Markov model".