A new model for on-line arithmetic with an application to the reciprocal calculation
Journal of Parallel and Distributed Computing
Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
An arithmetic unit for on-line computation.
An arithmetic unit for on-line computation.
Digit on-line algorithms for pipeline architectures
Digit on-line algorithms for pipeline architectures
On-the-Fly Algorithms and Sequential Machines
IEEE Transactions on Computers
On-line digit set conversion in real base
Theoretical Computer Science
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
On-line odometers for two-sided symbolic dynamical systems
DLT'02 Proceedings of the 6th international conference on Developments in language theory
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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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.