Issue No. 09 - September (2011 vol. 60)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2011.35
Nicholas Pippenger , Harvey Mudd College, Claremont
Frougny has presented a method that generalizes various "on-the-fly” operations that have been presented, mainly in connection with computer arithmetic. First, we shall trace the origin of this method to its source, which is the celebrated paper of Rabin and Scott that introduced the notion of nondeterminism and the power-set construction. Second, we shall show that an understanding of this origin may lead to great quantitative improvements in applications of the method. Finally, we shall show by a pathological example that the method as originally presented by Frougny may result in circuits that are larger, in terms of gates per step, by two exponentiations than those that are constructed as described in the present paper.
Finite automata, regular language, reversal.
N. Pippenger, "On-the-Fly Algorithms and Sequential Machines," in IEEE Transactions on Computers, vol. 60, no. , pp. 1372-1375, 2011.