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Some new procedures for designing efficient checking experiments for sequential machines are described. These procedures are based on the use of four types of sequences introduced, namely, the compound DS, the resolving sequence (RS), the compound. RS, and the simple I/O sequence. Significant reduction in the bound on the length of checking experiments is achieved. Along a parallel line of development, a new procedure, called the state counting method, is presented for detecting faults that can cause an increase in the number of states. For an n-state, m-input symbol machine, this procedure gives a bound on the length of checking experiments that is approximately mΔn. n times the bound for conventional checking experiments designed strictly under the assumption that no faults increase the number of states, where m > 1 and Δn is the maximum anticipated increase in the number of states due to faults.