An Improved Overlap Argument For On-Line Multiplication
| Citations: | 7 - 1 self |
BibTeX
@MISC{Paterson_animproved,
author = {Michael S. Paterson and Michael S. Paterson and Michael J. Fischer and Michael J. Fischer and Albert R. Meyer and Albert R. Meyer},
title = {An Improved Overlap Argument For On-Line Multiplication},
year = {}
}
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Abstract
A lower bound of cNlogN is proved for the mean time complexity of an on-line multitape Turing machine performing the multiplication of N-digit binary integers. For a more general class of machines which includes some models of random-access machines, the corresponding bound is cNlogN/loglogN. These bounds compare favorably with known upper bounds of the form cN(logN) k, and for some classes the upper and lower bounds coincide. The proofs are based on the "overlap" argument due to Cook and Aanderaa.
Citations
| 46 | On the Minimum Computation Time of Functions - Cook - 1966 |
| 12 | Real-time simulation of multi-head tape units - Fischer, Meyer, et al. - 1972 |
| 9 | A one-dimensional real-time iterative multiplier - Atrubin - 1965 |
| 3 | Fast on-line integer multiplication - Fischer, Stockmeyer - 1974 |
| 3 | Schnelle Multiplikation Grosser Zahlen, Commuting 7 - Schoenhage, Strassen - 1971 |
| 1 | On k-tape versus (k+l)-tape real-time computation, this volume - Aanderaa |
| 1 | Formal Laruaes and their Relation to Automata - Hopcroft, Ullman - 1969 |
