Causal analysis of positive Reaction Systems

Abstract

Cause/effect analysis of complex systems is instrumental in better understanding many natural phenomena. Moreover, formal analysis requires the availability of suitable abstract computational models that somehow preserve the features of interest. Our contribution focuses on the analysis of Reaction Systems (RSs), a qualitative computational formalism inspired by biochemical reactions in living cells. The primary challenge lies in dealing with inhibition mechanisms. On the one hand, inhibitors enhance the expressiveness of the computational abstraction; on the other hand, they can introduce nonmonotonic behaviors that can be computationally hard to deal with in the analysis. We propose an encoding of RSs into an equivalent formulation without inhibitors (called Positive RSs, PRSs for short) that is easier to handle, because PRSs exhibit monotonic behaviors. The effectiveness of our transformation is witnessed by its impact on two different techniques for cause/effect analysis. The first, called slicing, allows detecting the causes of some unforeseen phenomenon by reasoning backward along a given computation. Here, PRSs can be exploited to improve the quality of the analysis. The second technique, predictor analysis, is addressed by introducing a novel tool called MuMa, which is based on must/maybe sets, whence the tool name, an original abstraction for approximating ancestor formulas. MuMa exploits PRSs to improve the performance of the analysis.