Bahadur efficiency of a test of exponentiality based on the loss-of-memory property

A test of exponentiality of Kolmogorov–Smirnov type based on the loss-of-memory characterization property is under study. Large deviation asymptotics under the null-hypothesis is calculated. Local Bahadur efficiencies for commonly used parametric alternatives are found. Conditions of the Bahadur local optimality are obtained.