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Abstract:
We prove a separation bound for a large class of algebraic expressions
specified by expression dags.
The bound applies to expressions whose leaves are integers
and whose internal nodes are additions, subtractions, multiplications,
divisions, $k$-th root operations for integral $k$, and taking roots of
polynomials whose coefficients are given by the values of subexpressions.
The (logarithm of the)
new bound depends linearly on the algebraic degree of the expression.
Previous bounds applied to a smaller class of expressions and did not
guarantee linear dependency.
\ignore{In~\cite{BFMS} the dependency was quadratic.
and in the Li-Yap bound~\cite{LY} the dependency is usually linear, but may be
even worse than quadratic.}
