@article{ITA_1999__33_1_79_0,
author = {Frougny, Christiane},
title = {On-line finite automata for addition in some numeration systems},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {33},
year = {1999},
pages = {79-101},
mrnumber = {1705857},
zbl = {0927.68052},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_1999__33_1_79_0}
}
Frougny, Christiane. On-line finite automata for addition in some numeration systems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) pp. 79-101. http://gdmltest.u-ga.fr/item/ITA_1999__33_1_79_0/
[1] , , , , and , Automatic maps in exotic numeration systems. Theory Comput. Syst. 30 (1997) 285-331. | MR 1432196 | Zbl 0870.68105
[2] , and , Real/complex reconfigurable arithmetic using redundant complex number systems, in Proc. 13th Symposium on Computer Arithmetic (1997) 200-207.
[3] , Signed-digit number representations for fast parallel arithmetic. IEE Trans. Electron. Comput. 10 (1961) 389-400. | MR 135213
[4] , Codage symbolique, Masson (1993).
[5] , Transductions and Context-free Languages, Teubner (1979). | MR 549481 | Zbl 0424.68040
[6] , Fonctions rationnelles et addition. Actes de l'École de Printemps de Théorie des Langages, LITP (1982) 177-183.
[7] , Fibonacci words - A survey, The book of L, Springer-Verlag (1986) 13-27. | Zbl 0589.68053
[8] and , Logical design of a redundant binary adder, in Proc. 4th Symposium on Computer Arithmetic (1978) 109-115.
[9] , Une caractérisation des fonctions séquentielles et des fonctions sous-séquentielles en tant que relations rationnelles. Theoret. Comput. Sci. 5 (1977) 325-337. | MR 504457 | Zbl 0376.94022
[10] , and , New redundant representations of complex numbers and vectors. IEE Trans. Comput. C-42 (1993) 817-824. | MR 1252310
[11] , Automata, languages and machines, Vol. A (Academic Press, 1974). | MR 530382 | Zbl 0317.94045
[12] , On-line arithmetic: An overview. Real time Signal Processing VII SPIE 495 (1984) 86-93.
[13] , Confluent linear numeration systems. Theoret. Comput. Sci. 106 (1992) 183-219. | MR 1192767 | Zbl 0787.68057
[14] , Representation of numbers and finite automata. Math. Systems Theory 25 (1992) 37-60. | MR 1139094 | Zbl 0776.11005
[15] , 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] and , Synchronisation déterministe des automates à délai borné. Theoret. Comput. Sci. 191 (1998) 61-77. | MR 1490563 | Zbl 1015.68128
[17] , Radix representations of quadratic field. J. Math. Anal. Appl. 83 (1981) 264-274. | MR 632342 | Zbl 0472.10011
[18] , Contribution à l'arithmétique des ordinateurs, Ph. D. Dissertation, I.N.P.G., Grenoble, France (1991).
[19] and , Canonical number Systems. Acta Sci. Math. 37 (1975) 255-280. | MR 389759 | Zbl 0297.12003 | Zbl 0309.12001
[20] , An imaginary number system. CACM 3 (1960) 245-247. | MR 127508
[21] , The art of computer programming, Seminumerical Algorithms, Vol. 2, 2nd ed. (Addison-Wesley, 1988). | MR 378456
[22] , Classical number systems in Q[3√2]. Acta Sci. Math. 50 (1986) 351-357. | Zbl 0616.10007
[23] and , An introduction to symbolic dynamics and coding, Cambridge University Press (1995). | MR 1369092 | Zbl 1106.37301
[24] , Basic digit sets for radix representation. JACM 29 (1982) 1131-1143. | MR 674260 | Zbl 0509.10008
[25] , Some characterizations of fonctions computable in on-line arithmetic. IEE Trans. Comput. 43 (1994) 752-755. | MR 1284161 | Zbl 1042.68503
[26] and , Borrow-save adders for real and complex number systems, in Proc. of the Conference Real Numbers and Computers, Marseille (1996) 121-137.
[27] , Complex numbers multipliers. IEE Proc. Computers and Digital Techniques 136 (1989) 70-75.
[28] , A "binary" system for complex numbers. JACM 12 (1965) 247-248. | Zbl 0127.08803
[29] , Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar. 8 (1957) 477-493. | MR 97374 | Zbl 0079.08901
[30] , A good basis for computing with complex numbers. El. Math. 49 (1994) 111-117. | MR 1286599 | Zbl 0813.30001
[31] , Radix representations of algebraic number fields and finite automata, in Proc. Stacs'98, LNCS 1373 (1998) 356-365. | MR 1650694 | Zbl 0919.11009
[32] and , On-line algorithms for division and multiplication. IEE Trans. Comput. C 26 (1977) 681-687. | MR 451846 | Zbl 0406.68040
[33] , Addition molle et fonctions p-locales. Semigroup Forum 34 (1986) 157-175. | MR 868252 | Zbl 0605.68070