Automata Theory Meets Barrier Certificates: Temporal Logic Verification   of Nonlinear Systems
  We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based verification allows the decomposition the verification task into a finite collection of simpler constraints over the continuous state space. The satisfaction of these constraints in turn can be (potentially conservatively) proved by appropriately constructed barrier certificates. As a result, our approach, together with optimization-based search for barrier certificates, allows computational verification of dynamical systems against temporal logic properties while avoiding explicit abstractions of the dynamics as commonly done in literature. 
Tichakorn Wongpiromsarn, Ufuk Topcu and Andrew Lamperski
cs.FL cs.LO