On Superpolylogarithlnic Subexponential Functions (Part I)
Alan T. Sherman · ACM SIGACT News · 1991
A superpolylogarithmic subexponential function is any function that asymptotically grows faster than any polynomial of any logarithm but slower than any exponential. We present a recently discovered nineteenth-century manuscript about these functions, which in part because of their applications in cryptology, have received considerable attention in contemporary computer science research. Attributed to the little-known yet highly-suspect composer/mathematician Maria Poopings, the manuscript can be sung to the tune of "Supercalifragilisticexpialidocious" from the musical Mary Poppins. In addition, we prove three ridiculous facts about superpolylogarithmic subexponential functions. Using novel extensions to the popular DTIME notation from complexity theory, we also define the complexity class Super PolyLog/SubExp, which consists of all languages that can be accepted within deterministic superpolylogarithmic subexponential time. We show that this class is notationally intractable in the sense that it cannot be conveniently described using existing terminology. Surprisingly, there is some scientific value in our notational novelties; moreover, students may find this paper helpful in learning about growth rates, asymptotic notations, cryptology, and reversible computation.