Abstract
This paper develops a new and natural parallel vector model, and shows that for all k≥1, the languages recognizable in O(logkn) time and polynomial work in the model are exactly those in NCk. Some improvements to other simulations in parallel models and reversal complexity are given.
The author was supported in part by NSF Research Initiation Award CCR-9011248
Preview
Unable to display preview. Download preview PDF.
References
J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity Theory. Springer Verlag, 1988.
D. Mix Barrington. Bounded-width polynomial-size branching programs recognize exactly those languages in NC1. J. Comp. Sys. Sci., 38:150–164, 1989.
D. Mix Barrington, K. Compton, H. Straubing, and D. Thérien. Regular languages in NC1. J. Comp. Sys. Sci., 44:478–499, 1992.
D. Mix Barrington, N. Immerman, and H. Straubing. On uniformity within NC1. J. Comp. Sys. Sci., 41:274–306, 1990.
D. Mix Barrington and D. Thérien. Finite monoids and the fine structure of NC1. J. ACM, 35:941–952, 1988.
A. Chandra, S. Fortune, and R. Lipton. Unbounded fan-in circuits and associative functions. J. Comp. Sys. Sci., 30:222–234, 1985.
J. Chen and C. Yap. Reversal complexity. SIAM J. Comp., 20:622–638, 1991.
S. Cook. A taxonomy of problems with fast parallel algorithms. Info. Control, 64:2–22, 1985.
T. Harju, H.C.M. Klein, and M. Latteux. Deterministic sequential functions. Acta Informatics, 29:545–554, 1992.
J. Hartmanis, N. Immerman, and S. Mahaney. One-way log tape reductions. In Proc. 19th FOCS, pages 65–72, 1978.
J.-W. Hong. Computation: Similarity and Duality. Research Notes in Theoretical Computer Science. Wiley, 1986.
J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, MA, 1979.
T. Kameda and R. Vollmar. Note on tape reversal complexity of languages. Info. Control, 17:203–215, 1970.
R. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 871–941. Elsevier and MIT Press, 1990.
P. McKenzie, P. Péladeau, and D. Thérien. NC1: The automata-theoretic viewpoint. Computational Complexity, 1:330–359, 1991.
I. Parberry. An improved simulation of space and reversal bounded deterministic Turing machines by width and depth bounded uniform circuits. Inf. Proc. Lett., 24:363–367, 1987.
W. Paul, E. Prauss, and R. Reischuk. On alternation. Acta Informatica, 14:243–255, 1980.
N. Pippenger. On simultaneous resource bounds. In Proc. 20th FOCS, pages 307–311, 1979.
V. Pratt and L. Stockmeyer. A characterization of the power of vector machines. J. Comp. Sys. Sci., 12:198–221, 1976.
W. Ruzzo. On uniform circuit complexity. J. Comp. Sys. Sci., 22:365–373, 1981.
J. Simon. On some central problems in computational complexity. PhD thesis, Cornell University, 1975.
M. Sipser. Borel sets and circuit complexity. In Proc. 15th STOC, pages 61–69, 1983.
L. Stockmeyer and U. Vishkin. Simulations of parallel random access machines by circuits. SIAM J. Comp., 13:409–422, 1984.
J. Trahan, M. Loui, and V. Ramachandran. Multiplication, division, and shift instructions in parallel random access machines. Theor. Comp. Sci., 100:1–44, 1992.
P. van Emde Boas. Machine models and simulations. In J. Van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 1–66. Elsevier and MIT Press, 1990.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Regan, K.W. (1994). A new parallel vector model, with exact characterization of NCk . In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_149
Download citation
DOI: https://doi.org/10.1007/3-540-57785-8_149
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57785-0
Online ISBN: 978-3-540-48332-8
eBook Packages: Springer Book Archive