  This paper presents a methodology for temporal logic verification of
discrete-time stochastic systems. Our goal is to find a lower bound on the
probability that a complex temporal property is satisfied by finite traces of
the system. Desired temporal properties of the system are expressed using a
fragment of linear temporal logic, called safe LTL over finite traces. We
propose to use barrier certificates for computations of such lower bounds,
which is computationally much more efficient than the existing
discretization-based approaches. The new approach is discretization-free and
does not suffer from the curse of dimensionality caused by discretizing state
sets. The proposed approach relies on decomposing the negation of the
specification into a union of sequential reachabilities and then using barrier
certificates to compute upper bounds for these reachability probabilities. We
demonstrate the effectiveness of the proposed approach on case studies with
linear and polynomial dynamics.
