08w5094 Analytic Tools in Computational Complexity

Computational Complexity Theory is the field that studies the inherent costs of algorithms for solving mathematical problems. Its major goal is to identify the limits of what is efficiently computable in natural computational models. Computational complexity ranges from quantum computing to determining the minimum size of circuits that compute basic mathematical functions to the foundations of cryptography and security. Computational complexity emerged from the combination of logic, combinatorics, information theory, and operations research. It coalesced around the central problem of “P versus NP” (one of the seven open problems of the Clay Institute). While this problem remains open, the field has grown both in scope and sophistication. Currently, some of the most active research areas in computational complexity are