We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as JVP-complete… Expand

Two closely-related pseudo-random sequence generators are presented: The ${1 / P}$generator, with input P a prime, outputs the quotient digits obtained on dividing 1 by P. The $x^2 \bmod N$generato...Expand

In this paper we study volume estimates in the space of systems of n homegeneous polynomial equations of fixed degrees d i with respect to a natural Hermitian structure on the space of such systems… Expand

Let A be an n x n matrix whose elements are independent random variables with standard normal distributions. As n oo , the expected number of real eigenvalues is asymptotic to V/7r . We obtain a… Expand

We estimate the probability that a given number of projective Newton steps applied to a linear homotopy of a system of n homogeneous polynomial equations in $n + 1$ complex variables of fixed degrees… Expand