# The Operators min and max on the Polynomial Hierarchy

@article{Hempel1997TheOM, title={The Operators min and max on the Polynomial Hierarchy}, author={H. Hempel and G. Wechsung}, journal={Electron. Colloquium Comput. Complex.}, year={1997}, volume={4} }

Starting from Krentel's class OptP [Kre88] we define a general maximization operator max and a general minimization operator min for complexity classes and show that there are other interesting optimization classes beside OptP. We investigate the behavior of these operators on the polynomial hierarchy, in particular we study the inclusion structure of the classes max · P, max · NP, max · coNP, min · P, min · NP and min · coNP. Furthermore we prove some very powerful relations regarding the… Expand

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