Today the basic concepts of complexity theory are firmly ensconced in the bedrock of computer science, but that wasn't always the case. As late as 1965, computer scientists knew that some problems—such as finding an optimal schedule for airlines—seemed much more difficult than other problems: searching for a person's name in a sorted phonebook, for example. Computing professionals lacked the concepts to discuss these issues rigorously. They didn't even have the vocabulary.
That changed in 1965 when Juris Hartmanis and Richard E. Stearns published their groundbreaking paper "On the Computational Complexity of Algorithms." That article introduced the concept of a complexity class, providing a straightforward way to reason about complexity using multitape Turing machines, and mathematically proved that there are an infinite number of complexity classes. The paper set the stage for the discovery of space complexity later that year by the same authors, and of the NP-complete complexity class in 1971, independently by Stephen Cook and Leonid Levin.
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