Census algorithms for chinese remainder pseudorank
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 309-322.

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.

DOI : 10.1051/ita:2007024
Classification : 11Y99, 68R99
Mots clés : chinese remainder representation, rank, pseudorank, pseudorank census algorithms
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     author = {Laing, David and Litow, Bruce},
     title = {Census algorithms for chinese remainder pseudorank},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {309--322},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {2},
     year = {2008},
     doi = {10.1051/ita:2007024},
     mrnumber = {2401264},
     zbl = {1141.11324},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2007024/}
}
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Laing, David; Litow, Bruce. Census algorithms for chinese remainder pseudorank. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 2, pp. 309-322. doi : 10.1051/ita:2007024. http://www.numdam.org/articles/10.1051/ita:2007024/

[1] D.J. Bernstein and J. Sorenson, Modular exponentiation via the explicit chinese remainder theorem. Math. Comp. 76 (2007) 443-454. | MR

[2] A. Chiu, G. Davida and B. Litow, Division in logspace-uniform NC 1 . RAIRO-Theor. Inf. Appl. 35 (2001) 259-275. | Numdam | MR | Zbl

[3] G. Davida and B. Litow, Fast parallel arithmetic via modular representation. SIAM J. Comput. 20 (1991) 756-765. | MR | Zbl

[4] P. Dusart, The kth prime is greater than k(lnk-lnlnk-1) for k2. Math. Comp. 68 (1999) 411-415. | MR | Zbl

[5] G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers. Oxford Press, USA (1979). | JFM | MR | Zbl

[6] D. Knuth, The Art of Computer Programming, Vol. II. Addison-Wesley (1969). | MR | Zbl

[7] W. Kuich and A. Salomaa, Semirings, Automata, Languages. Springer-Verlag (1986). | MR | Zbl

[8] B. Litow and D. Laing, A census algorithm for chinese remainder pseudorank with experimental results. Technical Report. http://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). | MR | Zbl

[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). | MR

[11] I.M. Vinogradov, Elements of Number Theory. Dover (1954). | MR | Zbl

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