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<p>After a short introduction to on-line computing, we prove that the functions computable in on-line 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 bounded-size operators.</p>
digital arithmetic; finite automata; computability; online computing; finite automaton; piecewise affine functions; rational numbers; multiplication; division; elementary functions; operands; arbitrarily long length.
J.-M. Muller, "Some Characterizations of Functions Computable in On-Line Arithmetic", IEEE Transactions on Computers, vol. 43, no. , pp. 752-755, June 1994, doi:10.1109/12.286308
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