On Superpolylogarithlnic Subexponential Functions (Part I) * Alan T . Sherman Computer Science Departmen t University of Maryland Baltimore County Baltimore, Maryland 2122 8 and Institute for Advanced Computer Studie s University of Maryland College Park College Park, Maryland 2074 2 June 21, 199 0 (revised January 25, 1991 ) Abstract 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 o f their applications in cryptology, have received considerable attention in contemporary compute r science research . Attributed to the little-known yet highly-suspect composer/mathematicia n Maria Poopings, the manuscript can be sung to the tune of "Supercalifragilisticexpialidocious" from the musical Mary Pop pins . In addition, we prove three ridiculous facts about superpolylog arithmic subexponential functions . Using novel extensions to the popular DTIMD notation from complexity theory, we also define the complexity class SuperPolyLog/SubExp, which consist s of all languages that can be accepted within deterministic superpolylogarithmic subexponentia l time . We show that this class is notationally intractable in the sense that it cannot be conveniently described using
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On Superpolylogarithlnic Subexponential Functions (Part I)
Sherman, Alan T.
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, Volume 22 (1)
Association for Computing Machinery – Mar 1, 1991
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