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The authors define the notion of a lingering synchronisation effect. Such an effect occurs when a primary input cube (an incompletely specified primary input vector) determines the state of a circuit for several time units after it is applied. A primary input cube with a lingering synchronisation effect may prevent certain faults from being detected when it appears repeatedly in a test sequence. It should therefore be avoided when the goal is to achieve a high fault coverage. The authors demonstrate that benchmark circuits have primary input cubes with small numbers of specified values (typically one or two), which have lingering synchronisation effects. In some cases, the synchronisation effects linger for large numbers of time units. The authors define a ranking of primary input cubes based on the severity of their lingering synchronisation effects. They describe a random test generation process that avoids primary input cubes with lingering synchronisation effects, and achieves high fault coverage for benchmark circuits. The test generation process uses the severity of the lingering synchronisation effects of the primary input cubes to decide on the ones it should avoid.