Abstract
In this paper a definition of computability and complexity of real functions and real numbers is given which is open to methods of recursive function theory as well as to methods of numerical analysis. As an example of application we study the computational complexity of roots and thereby establish a subpolynomial hierarchy of real closed fields.
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Alt, H., Multiplication is the easiest nontrivial arithmetic function, Theoret. Comput. Sci. 36 (1985) 333–339
Brent, R.P., The complexity of multiple precision arithmetic, Proc. Seminar on Complexity of Computational Problem Solving, (Queensland U. Press, Brisbane, Australia, 1975) 126–165
Brent, R.P., Fast multiple precision evaluation of elementary functions, J. ACM 23 (1976) 242–251
Deil, T., Darstellungen und Berechenbarkeit reeler Zahlen, Informatik Berichte 51, Fern Universität Hagen (1984)
Ko, K. and Friedman, H., Computational complexity of real functions, Theoret. Comput. Sci. 20 (1982) 323–352
Kreitz, C., Theorie der Darstellungen und ihre Anwendung in der konstruktiven Analysis, Informatik Berichte 50, FernUniversität Hagen (1984)
Kreitz, C. and Weihrauch, K., Theory of representations, Theoret. Comput. Sci. 38 (1985) 35–53
Kreitz, C. and Weihrauch, K., Complexity theory on real numbers and real functions, Proc. 6th GI-Conf., Lecture notes in computer science 145 (Springer, Berlin, 1982) 165–174
Müller, N.Th., Computational complexity of real functions and real numbers, Informatik Berichte?, FernUniversität Hagen (to appear)
Owens, M.R., Compound algorithms for digit online arithmetic, Proc. 5th Symp. Comput. Arith., Ann Arbor, MI (1981) 64–71
Owens, M.R. and Irwin, M.J., On-line algorithms for the design of pipeline architectures, Proc. Annu. Symp. Comput. Arch., Philadelphia, PA (1979) 12–19
Paul, W.J., Komplexitätstheorie (Teubner, Stuttgart, 1978)
Schönhage, A., The fundamental theorem of algebra in terms of computational complexity, Preliminary Report, Mathematisches Institut der Universität Tübingen, 1982
Schönhage, A. and Strassen, V., Schnelle Multiplikation großer Zahlen, Computing 7 (1971) 281–292
Trivedi, K.S. and Ercegovac, M.D., On-line algorithms for division and multiplication, IEEE Trans. Comput., vol. C-26 (1977) 681–687
Weihrauch, K., Type 2 recursion theory, Theoret. Comput. Sci. 38 (1985) 17–33
Weihrauch, K., Computability (Springer, Berlin, to appear)
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© 1986 Springer-Verlag Berlin Heidelberg
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Müller, N.T. (1986). Subpolynomial complexity classes of real functions and real numbers. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_78
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DOI: https://doi.org/10.1007/3-540-16761-7_78
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