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Static timing analysis has traditionally used the PERT method for identifying the critical path of a circuit. The authors show in this paper that due to the influence of the transition time of a signal on the subsequent path delay, the traditional timing analysis approach can report an optimistic circuit delay and may identify the wrong critical path. Also, the calculated circuit delay is a discontinuous function with respect to transistor and gate sizes, posing a severe problem for circuit optimization methods. The authors also examine an alternate approach where the propagated signal is constructed by combining the latest arrival time and the slowest transition time from all signals incident on a node. While this approach remedies the problem of discontinuity, it can significantly overestimate the circuit delay and can also identify the wrong critical path. In this paper, they therefore propose a new timing analysis algorithm and prove that it computes the correct and continuous timing graph delay and the proper critical path. The proposed algorithm selectively propagates multiple signals through each timing edge in cases where there exists ambiguity regarding which arriving signal represents the critical path. They show that the algorithm propagates the sufficient and necessary set of signals for computing the delay of a general timing graph. The authors also introduce a new property of digital gates, referred to as the transition shift property, and, using this property, show that the number of propagated signals can be significantly reduced for timing graphs of digital circuits. Finally, they discuss the computation of required times and node slacks for the traditional approaches and propose corresponding algorithms for the new approaches. They show that while the traditional approach can incur both a positive or negative error in the computed slack, the proposed algorithms compute a conservative slack for off-critical nodes and the correct and continuous slack for the critical path. The proposed algorithms were implemented in an industrial static timing analysis and optimization tool, and the authors present results for a number of industrial circuits. Their results show that the traditional timing analysis method underestimates the circuit delay by as - much as 39%, while the discussed alternate approach can overestimate circuit delay by as much as 17%. The proposed method computes the correct delay, while incurring only a small run time overhead in all cases.