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The major contributions of this book are that we have provided a set of new concepts, innovative methods and algorithms for temporal verification in grid workflow systems. With these, we can significantly improve overall temporal verification effectiveness and efficiency. This would eventually improve the overall performance and usability of grid workflow systems because temporal verification can be viewed as a service or function of grid workflow systems. Consequently, by deploying the new concepts, innovative methods and algorithms, grid workflow systems would be able to better support large-scale sophisticated scientific and business processes in complex e-science and e-business applications in the context of grid economy.