On Closure Properties of #P in the Context of PF∘#P

摘要

For any operatorτon integer-valued functions, we say that #P isclosed under τ in the context ofPF∘#P if, for everyf∈#P,τ[f] belongs to PF∘num;P. For several operatorsτ, it is shown that the closure properties of #P underτin the above sense is closely related to the relationships between P#P[1]and higher classes such as PHPPand PPPP.