Totally Preset Checking Experiments for Sequential Machines

In this paper, we intoduce a new class of checking experiments, called uniform checking experiments, in which the entire input sequence, including the initialization part, is preset. The input sequence of a uniform checking experiment is called a uniform checking sequence. It is shown that every sequential machine possesses a uniform checking sequence. Trivially, if the machine has a synchronizing sequence, then the checking sequence constructed by employing any existent procedure is a uniform checking sequence. Some classes of machines which do not have synchronizing sequences are given and discussed. They are permutation machines, cycle machines, and symmetry machines. Different procedures for constructing efficient uniform checking sequences for them are then derived. It is found that while uniform checking sequences may be considerably longer than conventional checking sequences for arbitrary machines with no synchronizing sequences, the above classes of machines are shown to have uniform checking sequences comparable in length to conventional checking sequence.