Census algorithms for chinese remainder pseudorank

David Laing; Bruce Litow

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 42, Issue: 2, page 309-322
  • ISSN: 0988-3754

Abstract

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We investigate the density and distribution behaviors of the chinese remainder representation pseudorank. We give a very strong approximation to density, and derive two efficient algorithms to carry out an exact count (census) of the bad pseudorank integers. One of these algorithms has been implemented, giving results in excellent agreement with our density analysis out to 5189-bit integers.

How to cite

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Laing, David, and Litow, Bruce. "Census algorithms for chinese remainder pseudorank." RAIRO - Theoretical Informatics and Applications 42.2 (2007): 309-322. <http://eudml.org/doc/92873>.

@article{Laing2007,
abstract = { We investigate the density and distribution behaviors of the chinese remainder representation pseudorank. We give a very strong approximation to density, and derive two efficient algorithms to carry out an exact count (census) of the bad pseudorank integers. One of these algorithms has been implemented, giving results in excellent agreement with our density analysis out to 5189-bit integers. },
author = {Laing, David, Litow, Bruce},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Chinese remainder representation; rank; pseudorank; pseudorank census algorithms},
language = {eng},
month = {8},
number = {2},
pages = {309-322},
publisher = {EDP Sciences},
title = {Census algorithms for chinese remainder pseudorank},
url = {http://eudml.org/doc/92873},
volume = {42},
year = {2007},
}

TY - JOUR
AU - Laing, David
AU - Litow, Bruce
TI - Census algorithms for chinese remainder pseudorank
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/8//
PB - EDP Sciences
VL - 42
IS - 2
SP - 309
EP - 322
AB - We investigate the density and distribution behaviors of the chinese remainder representation pseudorank. We give a very strong approximation to density, and derive two efficient algorithms to carry out an exact count (census) of the bad pseudorank integers. One of these algorithms has been implemented, giving results in excellent agreement with our density analysis out to 5189-bit integers.
LA - eng
KW - Chinese remainder representation; rank; pseudorank; pseudorank census algorithms
UR - http://eudml.org/doc/92873
ER -

References

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  1. D.J. Bernstein and J. Sorenson, Modular exponentiation via the explicit chinese remainder theorem. Math. Comp.76 (2007) 443–454.  Zbl1183.11080
  2. A. Chiu, G. Davida and B. Litow, Division in logspace-uniform NC1. RAIRO-Theor. Inf. Appl.35 (2001) 259–275.  Zbl1014.68062
  3. G. Davida and B. Litow, Fast parallel arithmetic via modular representation. SIAM J. Comput.20 (1991) 756–765.  Zbl0736.68040
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  5. G.H. Hardy and E.M.Wright, An Introduction to the Theory of Numbers. Oxford Press, USA (1979).  Zbl0423.10001
  6. D. Knuth, The Art of Computer Programming, Vol. II. Addison-Wesley (1969).  Zbl0191.18001
  7. W. Kuich and A. Salomaa, Semirings, Automata, Languages. Springer-Verlag (1986).  
  8. B. Litow and D. Laing, A census algorithm for chinese remainder pseudorank with experimental results. Technical Report.  Zbl1141.11324URIhttp://www.it.jcu.edu.au/ftp/pub/techreports/2005-3.pdf
  9. A. Salomaa and S. Soittola, Automata Theoretic Aspects of Formal Power Series. Springer-Verlag (1978).  Zbl0377.68039
  10. S.P. Tarasov and M.N. Vyalyi, Semidefinite programming and arithmetic circuit evaluation. Technical report, arXiv:cs.CC/0512035 v1 9 Dec 2005 (2005).  Zbl1163.90694
  11. I.M. Vinogradov, Elements of Number Theory. Dover (1954).  Zbl0057.28201

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