Abstract
The problems of computing single-valued, analytic branches of the logarithm and square root functions on a bounded, simply connected domain S are studied. If the boundary \(\partial S\) of S is a polynomial-time computable Jordan curve, the complexity of these problems can be characterized by counting classes # P, MP (or MidBitP), and ā P: The logarithm problem is polynomial-time solvable if and only if FP=# P. For the square root problem, it has been shown to have the upper bound P MP and lower bound P āāāP. That is, if P=MP then the square root problem is polynomial-time solvable, and if \(P\not= \oplus P\) then the square root problem is not polynomial-time solvable.
This material is based upon work supported by National Science Foundation under grant No. 0430124.
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Ko, KI., Yu, F. (2005). On the Complexity of Computing the Logarithm and Square Root Functions on a Complex Domain. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_36
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DOI: https://doi.org/10.1007/11533719_36
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