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Up to now, few models of computation with the power of evaluating discon-tinuous functions have been analyzed and few of their lower bounds or results on the decidability of languages are known. In this paper, we present a model of an " analytic computation tree " (ACT). These trees operate on real numbers and are able to compare real numbers, to evaluate… (More)

- Bettina Just
- MFCS
- 1989

A vector m = (mx , ... , mn) eZ"\ {0} is called an integer relation for the real numbers a,, ... , an , if X)0,"1, = 0 holds. We present an algorithm that, when given algebraic numbers ax , ... , an and a parametere , either finds an integer relation for a,,... , an or proves that no relation of Euclidean length shorter than 1/e exists. Each algebraic… (More)

We consider computation trees (CTs) with operations $S \subset {+,-, *, DIV, DIV_c}$, where $DIV$ denotes integer division and $DIV_c$ integer division by constants. We characterize the families of languages $L \subset N$ that can be recognized over ${+,-, DIV_c}$ and ${+,-, *, DIV}$, resp. and show that they are identical. Furthermore, we prove lower… (More)

- P Elias, E V Hoversten, C E Shannon, R G Gallager, R S Kennedy, Jane W S Liu +19 others
- 2009

Let z be a non-negative, integer-valued random variable and let z i , 1 i < oo, be independent random variables, all having the same distribution as z. At t = 0 one particle is alive, and at t = 1 it gives birth to a random number z 1 of offspring. At t = 2 each of the z 1 first-generation particles gives birth to a random number (z 2 , z 3 , th .z +1) of… (More)

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