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Test complexity of generic polynomials
Citation key BLS-Test-Complexity-Of-Generic-Polynomials
Author Peter Bürgisser and Thomas Lickteig and Michael Shub
Pages 203-215
Year 1992
DOI 10.1016/0885-064X(92)90022-4
Journal J. Compl.
Volume 8
Number 3
Abstract We investigate the complexity of algebraic decision trees deciding membership in a hypersurface $X$ in $\mathbb C^m$. We prove an optimal lower bound on the number of additions, subtractions and comparisons and an asymptotically optimal lower bound on the number of multiplications, divisions and comparisons that are needed to decide membership in a generic hypersurface $X$ in $\mathbb C^m$. Over the reals, where in addition to equality branching also $<$-branching is allowed, we prove an analoguous statement for irreducible ``generic'' hypersurfaces $X$ in $\mathbb R^m$. In the case $m=1$ we give also a lower bound for finite subsets $X$ in $\mathbb R$.
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