On-line finite automata for addition in some numeration systems

Christiane Frougny

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1999)

  • Volume: 33, Issue: 1, page 79-101
  • ISSN: 0988-3754

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Frougny, Christiane. "On-line finite automata for addition in some numeration systems." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 33.1 (1999): 79-101. <http://eudml.org/doc/92592>.

@article{Frougny1999,
author = {Frougny, Christiane},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {numeration systems},
language = {eng},
number = {1},
pages = {79-101},
publisher = {EDP-Sciences},
title = {On-line finite automata for addition in some numeration systems},
url = {http://eudml.org/doc/92592},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Frougny, Christiane
TI - On-line finite automata for addition in some numeration systems
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1999
PB - EDP-Sciences
VL - 33
IS - 1
SP - 79
EP - 101
LA - eng
KW - numeration systems
UR - http://eudml.org/doc/92592
ER -

References

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  1. [1] J.-P. Allouche, E. Cateland, W. J. Gilbert, H.-O. Peitgen, J. O. Shallit and G. Skordev, Automatic maps in exotic numeration systems. Theory Comput. Syst. 30 (1997) 285-331. Zbl0870.68105MR1432196
  2. [2] T. Aoki, H. Amada and T. Higuchi, Real/complex reconfigurable arithmetic using redundant complex number systems, in Proc. 13th Symposium on Computer Arithmetic (1997) 200-207. 
  3. [3] A. Avizienis, Signed-digit number representations for fast parallel arithmetic. IEE Trans. Electron. Comput. 10 (1961) 389-400. MR135213
  4. [4] M. P. Béal, Codage symbolique, Masson (1993). 
  5. [5] J. Berstel, Transductions and Context-free Languages, Teubner (1979). Zbl0424.68040MR549481
  6. [6] J. Berstel, Fonctions rationnelles et addition. Actes de l'École de Printemps de Théorie des Langages, LITP (1982) 177-183. 
  7. [7] J. Berstel, Fibonacci words - A survey, The book of L, Springer-Verlag (1986) 13-27. Zbl0589.68053
  8. [8] C. Y. Chow and J. E. Robertson, Logical design of a redundant binary adder, in Proc. 4th Symposium on Computer Arithmetic (1978) 109-115. 
  9. [9] C. Choffrut, Une caractérisation des fonctions séquentielles et des fonctions sous-séquentielles en tant que relations rationnelles. Theoret. Comput. Sci. 5 (1977) 325-337. Zbl0376.94022MR504457
  10. [10] J. Duprat, Y. Herreros and S. Kla, New redundant representations of complex numbers and vectors. IEE Trans. Comput. C-42 (1993) 817-824. MR1252310
  11. [11] S. Eilenberg, Automata, languages and machines, Vol. A (Academic Press, 1974). Zbl0317.94045MR530382
  12. [12] M. D. Ercegovac, On-line arithmetic: An overview. Real time Signal Processing VII SPIE 495 (1984) 86-93. 
  13. [13] Ch. Frougny, Confluent linear numeration systems. Theoret. Comput. Sci. 106 (1992) 183-219. Zbl0787.68057MR1192767
  14. [14] Ch. Frougny, Representation of numbers and finite automata. Math. Systems Theory 25 (1992) 37-60. Zbl0776.11005MR1139094
  15. [15] Ch. Frougny, Parallel and on-line addition in negative base and some complex number systems, in Proc. of the Conference Euro-Par 96, Springer, Lyon, L.N.C.S. 1124 (1996) 175-182. 
  16. [16] Ch. Frougny and J. Sakarovitch, Synchronisation déterministe des automates à délai borné. Theoret. Comput. Sci. 191 (1998) 61-77. Zbl1015.68128MR1490563
  17. [17] W. Gilbert, Radix representations of quadratic field. J. Math. Anal. Appl. 83 (1981) 264-274. Zbl0472.10011MR632342
  18. [18] Y. Herreros, Contribution à l'arithmétique des ordinateurs, Ph. D. Dissertation, I.N.P.G., Grenoble, France (1991). 
  19. [19] I. Kátai and J. Szabó, Canonical number Systems. Acta Sci. Math. 37 (1975) 255-280. Zbl0309.12001MR389759
  20. [20] D. E. Knuth, An imaginary number system. CACM 3 (1960) 245-247. MR127508
  21. [21] D. E. Knuth, The art of computer programming, Seminumerical Algorithms, Vol. 2, 2nd ed. (Addison-Wesley, 1988). MR378456
  22. [22] S. Körmendi, Classical number systems in Q[3√2]. Acta Sci. Math. 50 (1986) 351-357. Zbl0616.10007
  23. [23] D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, Cambridge University Press (1995). Zbl1106.37301MR1369092
  24. [24] D. W. Matula, Basic digit sets for radix representation. JACM 29 (1982) 1131-1143. Zbl0509.10008MR674260
  25. [25] J.-M. Muller, Some characterizations of fonctions computable in on-line arithmetic. IEE Trans. Comput. 43 (1994) 752-755. Zbl1042.68503MR1284161
  26. [26] A. M. Nielsen and J.-M. Muller, Borrow-save adders for real and complex number systems, in Proc. of the Conference Real Numbers and Computers, Marseille (1996) 121-137. 
  27. [27] K. Pekmestzi, Complex numbers multipliers. IEE Proc. Computers and Digital Techniques 136 (1989) 70-75. 
  28. [28] W. Penney, A "binary" system for complex numbers. JACM 12 (1965) 247-248. Zbl0127.08803
  29. [29] A. Rényi, Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477-493. Zbl0079.08901MR97374
  30. [30] A. Robert, A good basis for computing with complex numbers. El. Math. 49 (1994) 111-117. Zbl0813.30001MR1286599
  31. [31] T. Safer, Radix representations of algebraic number fields and finite automata, in Proc. Stacs'98, LNCS 1373 (1998) 356-365. Zbl0919.11009MR1650694
  32. [32] K. S. Trivedi and M. D. Ercegovac, On-line algorithms for division and multiplication. IEE Trans. Comput. C 26 (1977) 681-687. Zbl0406.68040MR451846
  33. [33] O. Vaysse, Addition molle et fonctions p-locales. Semigroup Forum 34 (1986) 157-175. Zbl0605.68070MR868252

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