Abstract Interpretation for Probabilistic Termination of Biological Systems

In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology 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. In this paper, we refine the approach in order to address probabilistic termination properties. More in details, we introduce a refinement of the abstract LTS semantics and we abstract the probabilistic semantics using a variant of Interval Markov Chains. The abstract probabilistic model safely approximates a set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination.

💡 Research Summary

This paper presents a novel abstract‑interpretation framework for analyzing probabilistic termination properties of biochemical reaction networks modeled in the Chemical Ground Form (CGF) calculus. The authors build on their earlier work, which used interval abstraction of reagent multiplicities to capture families of experiments that differ only in initial concentrations. The current contribution refines that approach to address the quantitative question: “What is the probability that a system will reach a terminating state within a finite time?”

The methodology proceeds in four main steps. First, the CGF formalism is adopted because it provides a compact, compositional description of stochastic chemical reactions: each reaction is an atomic event with an exponential waiting time, yielding a continuous‑time Markov chain (CTMC) semantics. Second, the authors replace exact integer counts of each species with integer intervals (