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Complexity of computations
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Communications of the ACM archive
Volume 20 ,  Issue 9  (September 1977) table of contents
Pages: 625 - 633  
Year of Publication: 1977
ISSN:0001-0782
Author
Michael O. Rabin  Hebrew Univ. of Jerusalem, Jerusalem, Israel
Publisher
ACM  New York, NY, USA
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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

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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Brent, R,P. On the addition of binary numbers. IEEE Trans. Comptrs. C-19 (1970), 758-759.
 
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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.
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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.
 
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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.
 
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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.
 
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Meyer, A.R. The inherent computational complexity of theories of order. Proc. Int. Cong. Math., Vol. 2, Vancouver, 1974, pp. 477- 482.
 
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Motzkin, T.S. Evaluation of polynomials and evaluation of rational functions. Bull. Amer. Math. Soc. 61 (1955), 163.
 
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Munro, I., and Paterson, M. Optimal algorithms for parallel polynomial evaluation. J. Comptr. Syst. Sci., 7 (1973), 189-198.
 
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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.
 
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Rabin, M.O. Speed of computation and classification of recursive sets. Third Convention Sci. Soc., Israel, 1959, pp. 1-2.
 
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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.
 
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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.
 
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Sch6nhage, A., and Strassen, V. Schnelle Multiplication grosser Zahlen. Computing 7 (1971), 281-292.
 
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Strassen, V. Gaussian elimination is not optimal. Num. Math. 13 (1969), 354-356.
 
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Valiant, L.G. General context-free recognition in less than cubic time. Rep., Dept. Comptr. Sci., Carnegie-Mellon U., Pittsburgh, Pa., 1974.
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Winograd, S. On computing the discrete Fourier transform. Proc. Natl. Acad. Sci. USA 73 (1976), 1005-1006.