## Section: New Results

### Automated selection of PADE models by symbolic model checking

Participant : Grégory Batt.

Qualitative piecewise-affine differential equation (PADE) models offer an attractive formalism for representing genetic regulatory networks in absence of precise information on parameter values. Predictions on systems behaviors can be obtained in the form of a discrete state transition system simply by using parameter relative order.
In this work, we encode in a symbolic way the transition relation of the graph and use symbolic model checkers to automatically select the set of models whose parameter order is consistent with a set of observations.
Because in PADE systems the dynamics in a state may be defined with respect to the dynamics in neighbouring states, the main difficulty was to obtain a purely state-based encoding of the transition relation, similar to those used by model checkers.
This approach is applied to a synthetic gene network built in *E. coli* for *in vivo* benchmarking of reverse-engineering and modeling approaches (IRMA). This work is done in collaboration with Hidde de Jong and Michel Page in the IBIS research group (INRIA Rhône-Alpes/UPMF).