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Complexity of computations

Published:01 September 1977Publication History
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Abstract

The framework for research in the theory of complexity of computations is described, emphasizing the interrelation between seemingly diverse problems and methods. Illustrative examples of practical and theoretical significance are given. Directions for new research are discussed.

References

  1. 1 Blum, M, A machine independent theory of the complexity of recursive functions. J. ACM 14 (1967), 322-336. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2 Brent, R,P. On the addition of binary numbers. IEEE Trans. Comptrs. C-19 (1970), 758-759.Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3 Brent, R.P. The parallel evaluation of algebraic expressions in logarithmic time. Complexity of Sequential and Parallel Numerical Algorithms, J.F. Traub, Ed., Academic Press, New York, 1973, pp. 83-102.Google ScholarGoogle Scholar
  4. 4 Cook, S.A. The complexity of theorem proving procedures. Proc. Third Annual ACM Symp. on Theory of Comptng., 1971, pp. 151-158. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5 Fischer, M.J., and Rabin, M.O. Super-exponential complexity of Presburger arithmetic. In Complexity of Computations (SIAM- AMS Proc., Vol. 7), R.M. Karp Ed., 1974, pp. 27-41.Google ScholarGoogle Scholar
  6. 6 Floyd, R.W. Permuting information in idealized two-level storage. In Complexity of Computer Computations, R. Miller and J. Thatcher Eds., Plenum Press, New York, 1972, pp. 105-109.Google ScholarGoogle ScholarCross RefCross Ref
  7. 7 Karp, R.M. Reducibility among combinatorial problems. In Complexity of Computer Computations, R. Miller and J. Thatcher Eds., Plenum Press, New York, 1972, pp. 85-103.Google ScholarGoogle ScholarCross RefCross Ref
  8. 8 Meyer, A.R. The inherent computational complexity of theories of order. Proc. Int. Cong. Math., Vol. 2, Vancouver, 1974, pp. 477- 482.Google ScholarGoogle Scholar
  9. 9 Motzkin, T.S. Evaluation of polynomials and evaluation of rational functions. Bull. Amer. Math. Soc. 61 (1955), 163.Google ScholarGoogle Scholar
  10. 10 Munro, I., and Paterson, M. Optimal algorithms for parallel polynomial evaluation. J. Comptr. Syst. Sci., 7 (1973), 189-198.Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11 Paterson, M., Fischer, M.J., and Meyer, A.R. An improved overlap argument for on-line multiplication. Proj. MAC Tech. Report 40, M.I.T. (1974). Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12 Presburger, M. Uber die Vollstfindigkeit eines gewissea Systems Arithmetic ganzer Zahlen in welchem die Addition als eiilzige Operation hervortritt. Comptes-rendus du I Congr~s de Mathematiciens de Pays Slaves, Warsaw, 1930, pp. 92-101,395.Google ScholarGoogle Scholar
  13. 13 Rabin, M.O. Speed of computation and classification of recursive sets. Third Convention Sci. Soc., Israel, 1959, pp. 1-2.Google ScholarGoogle Scholar
  14. 14 Rabin, M.O. Degree of difficulty of computing a function and a partial ordering of recursive sets. Tech. Rep. No. 1, O.N,R., Jerusalem, 1960.Google ScholarGoogle Scholar
  15. 15 Rabin, M.O. Probabilistic algorithms. In Algorithms and Complexity, New Directions and Recent Trends, J .F. Traub Ed., Academic Press, New York, 1976, pp. 21-39.Google ScholarGoogle Scholar
  16. 16 Sch6nhage, A., and Strassen, V. Schnelle Multiplication grosser Zahlen. Computing 7 (1971), 281-292.Google ScholarGoogle ScholarCross RefCross Ref
  17. 17 Strassen, V. Gaussian elimination is not optimal. Num. Math. 13 (1969), 354-356.Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. 18 Valiant, L.G. General context-free recognition in less than cubic time. Rep., Dept. Comptr. Sci., Carnegie-Mellon U., Pittsburgh, Pa., 1974.Google ScholarGoogle Scholar
  19. 19 Winograd, S. On the time required to perform addition. J. ACM 12 (1965), 277-285. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. 20 Winograd, S. On computing the discrete Fourier transform. Proc. Natl. Acad. Sci. USA 73 (1976), 1005-1006.Google ScholarGoogle ScholarCross RefCross Ref

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                cover image Communications of the ACM
                Communications of the ACM  Volume 20, Issue 9
                Sept. 1977
                60 pages
                ISSN:0001-0782
                EISSN:1557-7317
                DOI:10.1145/359810
                Issue’s Table of Contents

                Copyright © 1977 ACM

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                Association for Computing Machinery

                New York, NY, United States

                Publication History

                • Published: 1 September 1977

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