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J.M. Muller, "Some Characterizations of Functions Computable in OnLine Arithmetic," IEEE Transactions on Computers, vol. 43, no. 6, pp. 752755, June, 1994.  
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@article{ 10.1109/12.286308, author = {J.M. Muller}, title = {Some Characterizations of Functions Computable in OnLine Arithmetic}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {6}, issn = {00189340}, year = {1994}, pages = {752755}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.286308}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Some Characterizations of Functions Computable in OnLine Arithmetic IS  6 SN  00189340 SP752 EP755 EPD  752755 A1  J.M. Muller, PY  1994 KW  digital arithmetic; finite automata; computability; online computing; finite automaton; piecewise affine functions; rational numbers; multiplication; division; elementary functions; operands; arbitrarily long length. VL  43 JA  IEEE Transactions on Computers ER   
After a short introduction to online computing, we prove that the functions computable in online by a finite automaton are piecewise affine functions whose coefficients are rational numbers (i.e., the functions f(x)=ax+b, or f(x,y)=ax+by+c where a, b, and c are rational). A consequence of this study is that multiplication, division and elementary functions of operands of arbitrarily long length cannot be performed using boundedsize operators.
[1] A. Avizienis, "Signeddigit number representations for fast parallel arithmetic,"IRE Trans. Electron. Comput., vol. 10, pp. 389400, 1961.
[2] M. D. Ercegovac and K. S. Trivedi, "On line algorithms for division and multiplication,"IEEE Trans. Comput., vol. C26, no. 7, pp. 681687, July 1977.
[3] M. D. Ercegovac and P. K. G. Tu, "A radix4 online division algorithm," presented at8th Symp. Comput. Arithmetic, Como, Italy, May 1987.
[4] M. J. Irwin and R. M. Owens, "Digit pipelined arithmetic as illustrated by the pasteup system,"IEEE Comput. Mag., pp. 6173, Apr. 1987.
[5] M. J. Irwin, "An arithmetic unit for Online computation," Ph.D. dissertation, Dept. of Comput. Sci., Univ. of Illinois, ChampaignUrbana, IL; Tech. Rep. UIUCDCSR77873, 1977.
[6] J. G. Rusnak and K. S. Trivedi, "Higher radix online division," inProc. 4th IEEE Symp. Comput. Arithmetic, Oct. 1978, pp. 183189.
[7] M. D. Ercegovac, "An online square rooting algorithm," inProc. 4th IEEE Symp. Comput. Arithmetic, Oct. 1978, pp. 183189.
[8] R. M. Owens, "Digit online algorithms for pipelined architectures," Ph.D. dissertation, Dep. Comput. Sci., The Pennsylvania State Univ., 1980.
[9] M. D. Ercegovac, "Online arithmetic: An overview,"SPIE, vol. 495,Real Time Signal ProcessingVII, 1984, pp. 8693.
[10] R. M. Owens, "Techniques to reduce the inherent limitations of fully digit online arithmetic,"IEEE Trans. Comput., vol. C32, no. 4, Apr. 1983.
[11] H. J. Sips and H. X. Lin, "A new model for online arithmetic with an application to the reciprocal calculation,"J. Parallel Distributed Comput., pp. 218230, 1990.
[12] J. Duprat, Y. Herreros, and J. M. Muller, "Some results about online computation of functions," inProc. 9th Symp. Comput. Arithmetic, Santa Monica, CA, Sept. 1989, pp. 112118.
[13] E. Wiedmer, "Computing with infinite objects,"Theorem Comput. Sci., vol. 10, pp. 133155, 1980.
[14] J. Vuillemin, "Exact real computer arithmetic with continued fractions,"IEEE Trans. Comput., vol. 39, no. 8, pp. 10871105, Aug. 1990.