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Timing analysis is critical for many circuit optimizations. An accurate timing analysis can be achieved by finding input vectors that simultaneously satisfy both functional and temporal requirements. The problem of finding such input vectors can be modeled as a Boolean equation called the timed characteristic function (TCF). Despite the usefulness of the TCF, traditional TCF construction and solving is slow for large circuits. In this paper, we present a more efficient way to use the TCF. On average, our method is much faster than other most recent works.