There are two main shortcomings in the existing models for generating checking sequences based on distinguishing sequences. First, these models require a priori selection of state recognition sequences (called
-sequences) which may not be the best selection for yielding substantial reduction in the length of checking sequences. Second, they do not take advantage of overlapping to further reduce the length of checking sequences. This paper proposes an optimization model that tackles these shortcomings to reduce the lengths of checking sequences beyond what is achieved by the existing models by replacing the state recognition sequences with a set of basic sequences called
-elements and by making use of overlapping.