Title: Approximation Techniques for Stochastic Analysis of Biological Systems,
Abstract: There has been an increasing demand for formal methods in the design process
of safety-critical synthetic genetic circuits. Probabilistic model checking
techniques have demonstrated significant potential in analyzing the intrinsic
probabilistic behaviors of complex genetic circuit designs. However, its
inability to scale limits its applicability in practice. This chapter addresses
the scalability problem by presenting a state-space approximation method to
remove unlikely states resulting in a reduced, finite state representation of
the infinite-state continuous-time Markov chain that is amenable to
probabilistic model checking. The proposed method is evaluated on a design of a
genetic toggle switch. Comparisons with another state-of-art tool demonstrates
both accuracy and efficiency of the presented method.