Using Distinguishing and UIO Sequences Together in a Checking Sequence

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If a finite state machine M does not have a distinguishing sequence, but has UIO sequences for its states, there are methods to produce a checking sequence for M. However, if M has a distinguishing sequence $\bar{D}$ , then there are methods that make use of $\bar{D}$ to construct checking sequences that are much shorter than the ones that would be constructed by using only the UIO sequences for M. The methods to applied when a distinguishing sequence exists, only make use of the distinguishing sequences. In this paper we show that, even if M has a distinguishing sequence $\bar{D}$ , the UIO sequences can still be used together with $\bar{D}$ to construct shorter checking sequences.