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Time-space tradeoff lower bounds for integer . . . (Extended Abstract) (2003)
| Citations: | 8 - 2 self |
BibTeX
@MISC{Sauerhoff03time-spacetradeoff,
author = {Martin Sauerhoff and et al.},
title = { Time-space tradeoff lower bounds for integer . . . (Extended Abstract)},
year = {2003}
}
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Abstract
We prove exponential size lower bounds for nondeterministic and randomized read-k BPs as well as a time-space tradeoff lower bound for unrestricted, deterministic multi-way BPs computing the middle bit of integer multiplication. The lower bound for randomized read-k BPs is superpolynomial as long as the error probability is superpolynomially small. For polynomially small error, we have a polynomial upper bound on the size of approximating read-once BPs for this function. The lower bounds follow from a more general result for the graphs of universal hash classes that is applicable to the graphs of arithmetic functions such as integer multiplication, convolution, and finite field multiplication.
Keyphrases
time-space tradeoff extended abstract randomized read-k bps integer multiplication small error deterministic multi-way bps read-once bps universal hash class exponential size general result error probability arithmetic function polynomial upper bound middle bit finite field multiplication
