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Digital Logic Design: A Rigorous Approach by Moti Medina, Guy Even

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CHAPTER 7

Asymptotics

In this chapter, we study the rate of growth of positive sequences. We introduce a formal definition that enables us to say that one sequence does not grow faster than another sequence. Suppose we have two sequences images and images. We could say that xi does not grow faster than yi if xiyi for every i. However, such a restricted definition is rather limited, as suggested by the following examples:

  1. The sequence xi is constant: xi = 1000 for every i, while the sequence yi is defined by yi = i. Clearly we would like to say that ...

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