This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Adleman, L. Two theorems on random polynomial time, Proc. 19th IEEE FOCS (1978), 75–83.
Aho, A.V., Hopcroft, J.E. and Ullman, J.D. The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, Mass. (1974).
Awerbuch, B. and Shiloach, Y. New connectivity and MSF algorithms for Ultracomputer and PRAM. Preprint, IBM-Israel Scientific Center, Technion, Haifa (1983).
Beame, P.W., Cook, S.A. and Hoover, H.J. Small depth circuits for integer products, powers, and division. Preprint (1983).
Berkowitz, S.J. On computing the determinant in small parallel time using a small number of processors. Preprint (1982).
Borodin, A. On relating time and space to size and depth, SIAM J. Comput. 6(1977), 733–744.
Borodin, A., Cook, S.A. and Pippenger, N. Parallel computation for well-endowed rings and space-bounded probabilistic machines. Technical Report 162/83, Department of Computer Science, University of Toronto (1983).
Borodin, A., von zur Gathen, J. and Hopcroft, J. Fast parallel matrix and GCD computations, Proc. 23rd IEEE FOCS (1982), 65–71.
Chandra, A.K., Kozen, D.C. and Stockmeyer, L.J. Alternation, J. ACM 28, 1(Jan. 1981), 114–133.
Chandra, A.K., Stockmeyer, L.J. and Vishkin, U. Complexity theory for unbounded fan-in parallelism, Proc. 23rd IEEE FOCS (1982), 1–13.
Cook, S.A. Towards a complexity theory of synchronous parallel computation, L'Enseignement Mathematique XXVII (1981), 99–124.
Cook, S.A., Ruzzo, W.L. and Tompa, M. "Oral theorem" (1983).
Csanky, L. Fast parallel matrix inversion algorithms, SIAM J. Comput. 5(1976), 618–623.
Dobkin, D., Lipton, R.J. and Reiss, S. Linear programming is log-space hard for P, Information Processing Letters 8(1979), 96–97.
Dymond, P.W. and Cook, S.A. Hardware Complexity and Parallel Computation, Proc. 21st IEEE FOCS (1980), 360–372.
Feather, T. M.Sc. thesis, Department of Computer Science, University of Toronto. To appear.
Furst, M., Saxe, J., Sipser, M. Parity, circuits, and the polynomial-time hierarchy, Proc. 22nd IEEE FOCS (1981), 260–270.
Garey, M.R. and Johnson, D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, San Francisco (1979).
von zur Gathen, J. Parallel algorithms for algebraic problems, Proc. 15th ACM STOC (1983), 17–23.
Gill, J. Computational complexity of probabilistic Turing machines, SIAM J. Comput. 6(1977), 675–695.
Goldschlager, L.M. Synchronous Parallel Computation, Ph.D. Thesis, University of Toronto (1977). See also Proc. 10th ACM STOC (1978), 89–94 and J. ACM 29, 4(Oct. 1982), 1073–1086.
Goldschlager, L.M. The monotone and planar circuit value problems are log space complete for P, SIGACT News 9, 2(summer 1977), 25–29.
Goldschlager, L.M., Shaw, R.A. and Staples, J. The maximum flow problem is log space complete for P, Theoretical Computer Science 21(1982), 105–111.
Hong, J.W. On some space complexity problems about the set of assignments satisfying a boolean formula, Proc. 12th ACM STOC (1980), 310–317.
Hoover, H.J. Some Topics in Circuit Complexity, M.Sc. Thesis, University of Toronto, Department of Computer Science (1979). Also available as Department of Computer Science Technical Report 139/80.
Ibarra, O.H., Moran, S. and Rosier, L.E. A note on the parallel complexity of computing the rank of order n matrices, Information Processing Letters 11(1980), 162.
Ja' Ja', J. and Simon, J. Parallel algorithms in graph theory: planarity testing, SIAM J. Comput. 11(1982), 314–328.
Jones, N.D. and Laaser, W.T. Complete problems for deterministic polynomial time, Theoretical Computer Science 3(1977), 105–117.
Khachian, L.G. A polynomial time algorithm for linear programming, Doklady Akad. Nauk SSSR, 244, 5(1979), 1093–96. Translated in Soviet Math. Doklady, 20, 191–194.
Ladner, R.E. The circuit value problem is log space complete for P, SIGACT News 7, 1(1975), 18–20.
Lev., G. Size bounds and parallel algorithms for networks, Doctoral Thesis, Report CST-8-80, Dept. of Computer Science, University of Edinburgh (1980).
Lynch, N. Log space recognition and translation of parenthesis languages, J. ACM 24 4(Oct. 1977), 583–590.
McKenzie, P. and Cook, S.A. Parallel complexity of the Abelian permutation group membership problem. Extended abstract (1983).
Muller, D.E. and Preparata, F.P. Bounds to complexities of networks for sorting and switching, J. ACM 22, 2(April 1975), 195–201.
Pippenger, N. On simultaneous resource bounds (preliminary version), Proc. 20th IEEE FOCS (1979), 307–311.
Papadimitriou, C.H. and Steiglitz, K. Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ (1982).
Pippenger, N. On simultaneous resource bounds (preliminary version), Proc. 20th IEEE FOCS (1979), 307–311.
Reif, J.H. Symmetric complementation, Proc. 14th ACM STOC (1982), 201–214.
Reif, J.H. Logarithmic depth circuits for algebraic functions, TR-35-82, Aiken Computation Laboratory, Harvard University (Nov. 1982).
Ruzzo, W.L. Unpublished list of problems in NC 2 (1980).
Ruzzo, W.L. Tree-size bounded alternation, Journal of Computer and System Sciences 21, 2(Oct. 1980), 218–235.
Ruzzo, W.L. On uniform circuit complexity, Journal of Computer and System Sciences 22, 3(June 1981), 365–383.
Ruzzo, W.L. and Tompa, M. Unpublished result (1982). See Stockmeyer, L. and Viskin, U. Simulation of parallel random access machines by circuits, Report RC-9362, IBM Research, Yorktown Heights, NY.
Savage, J.E. The Complexity of Computing, Wiley, New York (1976).
Schwartz, J.T. Ultracomputers, ACM Trans. on Prog. Languages and Systems 2, 4(Oct. 1980), 484–521.
Schwartz, J.T. Probabilistic algorithms for verification of polynomial identifies, J. ACM 27, 4(Oct. 1980), 701–717.
Shannon, C.E. The synthesis of two terminal switching circuits, BSTJ 28(1949), 59–98.
Sudborough, I.H. On the tape complexity of deterministic context-free languages, J. ACM 25, 3(July 1978), 405–414.
Valiant, L.G. Completeness classes in algebra, Proc. 11th ACM STOC (1979), 249–261.
Valiant, L.G., Skyum, S., Berkowitz, S. and Rackoff, C. Fast parallel computation on polynomials using few processors. Preprint. Preliminary version in Springer Lecture Notes in Computer Science, 118(1981), 132–139.
Vishkin, U. Synchronous parallel computation — a survey. Preprint, Courant Institute, New York University (1983).
Wilson, C. Preprint (1982).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cook, S.A. (1983). The classification of problems which have fast parallel algorithms. In: Karpinski, M. (eds) Foundations of Computation Theory. FCT 1983. Lecture Notes in Computer Science, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12689-9_95
Download citation
DOI: https://doi.org/10.1007/3-540-12689-9_95
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12689-8
Online ISBN: 978-3-540-38682-7
eBook Packages: Springer Book Archive