  We address the problem of detecting and mitigating the effect of malicious
attacks to the sensors of a linear dynamical system. We develop a novel,
efficient algorithm that uses a Satisfiability-Modulo-Theory approach to
isolate the compromised sensors and estimate the system state despite the
presence of the attack, thus harnessing the intrinsic combinatorial complexity
of the problem. By leveraging results from formal methods over real numbers, we
provide guarantees on the soundness and completeness of our algorithm. We then
report simulation results to compare its runtime performance with alternative
techniques. Finally, we demonstrate its application to the problem of
controlling an unmanned ground vehicle.
