An Analysis for Proving Probabilistic Termination of Biological Systems

In this paper we apply the abstract interpretation approach for approximating the behavior of biological systems, modeled specifically using the Chemical Ground Form calculus, a simple stochastic calculus rich enough to model the dynamics of biochemical reactions. The analysis is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. For abstracting the probabilistic semantics, modeled as a Discrete-Time Markov Chain, we use a variant of Interval Markov Chains, where probabilistic and non-deterministic steps are combined together. The abstract probabilistic semantics is systematically derived from an abstract Labeled Transition System. The abstract probabilistic model safely approximates the set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination.