## Section: Overall Objectives

### Highlight: Parameter Optimization w.r.t. Temporal Logic Constraints

Temporal logics and model-checking are at the core of our approach in BIOCHAM to express biological properties of complex biochemical systems and automatically verify their satisfaction in both qualitative and quantitative models. Last year, we introduced a fundamental generalization of model-checking to constraint solving by presenting a constraint solving algorithm for quantifier-free first-order temporal logic formulae with constraints over the reals, denoted by QFLTL(R). This algorithm computes the domain of the real valued variables occurring in a QFLTL(R) formula that makes it true in a model [3] , [16] .

Based on this result, we are now able to define a continuous degree of satisfaction of LTL(R) formulae in a given trace, as a distance to the validity domain of a corresponding QFLTL(R) formula. This opens up the field of continuous optimization methods to parameter search w.r.t. high-level specifications in temporal logic.

In [22] , we show how this approach applies to searching several tenths of kinetic parameters from high-level specifications in reaction models of the cell cycle and of the MAPK signalling cascade (37 parameters). The Covariance Matrix Adaptation Evolutionary Strategy CMAES of Nikolaus Hansen from the TAO team used in these experiments let us hope to deal with a hundred of parameters.