MDDs Boost Equation Solving on Discrete Dynamical Systems

Discrete dynamical systems (DDS) are a model to represent complex phenomena appearing in many different domains. In the finite case, they can be identified with a particular class of graphs called dynamics graphs. In [9] polynomial equations over dynamics graphs have been introduced. A polynomial equation represents a hypothesis on the fine structure of the system. Finding the solutions of such equations validate or invalidate the hypothesis. This paper proposes new algorithms that enumerate all the solutions of polynomial equations with constant right-hand term outperforming the current state-of-art methods [10]. The boost in performance of our algorithms comes essentially from a clever usage of Multi-valued decision diagrams. These results are an important step forward in the analysis of complex dynamics graphs as those appearing, for instance, in biological regulatory networks or in systems biology.