The Operators min and max on the Polynomial Hierarchy

@article{Hempel2000TheOM,
  title={The Operators min and max on the Polynomial Hierarchy},
  author={H. Hempel and G. Wechsung},
  journal={Int. J. Found. Comput. Sci.},
  year={2000},
  volume={11},
  pages={315-342}
}
By defining a general max and a general min operator for complexity classes we obtain that there are other interesting classes of optimization functions besides Krentel's class 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. It turns out that our operators when applied to the polynomial hierarchy yield a refinement of Krentel's… Expand
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