  Boolean automata networks, genetic regulation networks, and metabolic
networks are just a few examples of biological modelling by discrete dynamical
systems (DDS). A major issue in modelling is the verification of the model
against the experimental data or inducing the model under uncertainties in the
data. Equipping finite discrete dynamical systems with an algebraic structure
of commutative semiring provides a suitable context for hypothesis verification
on the dynamics of DDS. Indeed, hypothesis on the systems can be translated
into polynomial equations over DDS. Solutions to these equations provide the
validation to the initial hypothesis. Unfortunately, finding solutions to
general equations over DDS is undecidable. In this article, we want to push the
envelope further by proposing a practical approach for some decidable cases in
a suitable configuration that we call the Hypothesis Checking. We demonstrate
that for many decidable equations all boils down to a "simpler" equation.
However, the problem is not to decide if the simple equation has a solution,
but to enumerate all the solutions in order to verify the hypothesis on the
real and undecidable systems. We evaluate experimentally our approach and show
that it has good scalability properties.
