Rare events in stochastic dynamical systems and failures in ultra-reliable reactive programs

Reactive programs are a class of software whose behavior is highly dependent on the environment. For such programs, the successive inputs are not independent, due to the continuity of the physical behavior of the system under control. This paper presents a model of such programs and of their failures, based on stochastic processes. Then, exploiting some results on rare events in mixing dynamical systems we state a rigorous result concerning the asymptotical distribution of the time to failure in this kind of program. This result says that this distribution can be approximated in a sharp way by an exponential distribution. Moreover, the more reliable is the program, the sharper is the approximation.