The satanic notations: counting classes beyond #P and other definitional adventures

@article{Hemaspaandra1995TheSN,
  title={The satanic notations: counting classes beyond #P and other definitional adventures},
  author={Lane A. Hemaspaandra and Heribert Vollmer},
  journal={SIGACT News},
  year={1995},
  volume={26},
  pages={2-13}
}
We explore the potentially "off-by-one" nature of the definitions of counting (#P versus #NP), difference (DP versus DNP), and unambiguous (UP versus UNP; FewP versus FewNP) classes, and make suggestions as to logical approaches in each case. We discuss the strangely differing representations that oracle and predicate models give for counting classes, and we survey the properties of counting classes beyond #P. We ask whether subtracting a #P function from a P function it is no greater than… CONTINUE READING