Thomas Jerome Schaefer
Thomas Jerome Schaefer is an American mathematician. He obtained his Ph.D. in December 1978 from the University of California, Berkeley, where he worked in the Department of Mathematics. His Ph.D. advisor was Richard M. Karp. He is well-known for his dichotomy theorem, stating that any problem generalizing Boolean satisfiability in a certain way is either in the complexity class P or is NP-complete In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by tryi .... References Year of birth missing (living people) Living people 20th-century American mathematicians American computer scientists University of California, Berkeley alumni 21st-century American mathematicians {{US-mathematician-stub ...
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Computational Complexity Theory
In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying their computational complexity, i.e., the amount of resources needed to solve them, such as time and storage. Other measures of complexity are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computationa ...
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