Evolution time of stochastic systems with multiple final sequences of states

A stochastic system with multiple final sequences of states represents a stochastic system that stops its evolution as soon as one of the given final sequences of states is reached. The transition time of the system is unitary and the transition probability depends on source and destination states. We prove that the distribution of the evolution time is a homogeneous linear recurrent sequence and, based on this, a polynomial algorithm for determining the initial state and the generating vector of this recurrence is developed. Using the generating function, the main probabilistic characteristics are determined.