## Section: Overall Objectives

### Highlight: Model-checking generalized to constraint solving

In [16] , we present a fundamental generalization of model-checking to temporal logic constraint solving, by considering temporal logic formulae with free variables over some domain D , and by computing a validity domain for the variables rather than a truth value for the formula. When D is a metric space, this allows us to define a continuous degree of satisfaction for a temporal logic formula in a given Kripke structure, opening up the field of model-checking to optimization.

This work originates from previous work in BIOCHAM on reverse engineering problems coming from systems biology. The algorithm used in BIOCHAM for solving Linear Time Logic constraints over the reals (LTL(R )) has been generalized to a fixpoint algorithm for branching time logics, namely for the quantifier-free first-order Computation Tree Logic over some arbitrary domain D (QFCTL(D )).

Our result shows that any constraint solver over some domain D can be lifted to a QFCTL(D ) constraint solver over a finite Kripke structure over D , and that optimization techniques can be used to synthesize or parameterize deterministic as well as non-deterministic systems, in order to satisfy high-level QFCTL(D ) specifications.