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LOC is sequential, since it is essentially a double capture, and the ATPG tool needs to be able to store the state of the circuit after the last shift and first clock pulse of the capture in order to know what is expected after the second capture clock.
LOS is essentially the same as a simple stuck-at, since there is only one clock pulse during the capture. No second state needs to be stored by the ATPG to determine how the circuit will react after the second clock pulse.
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