TU Berlin

Fachgebiet Algorithmische AlgebraPublications

Page Content

to Navigation

There is no English translation for this web page.

Search for Publication

Search for publications

All Publications

On randomized semialgebraic decision complexity
Citation key BKL-On-Randomized-Semialgebraic-Decision-Complexity
Author Peter Bürgisser and Marek Karpinski and Thomas Lickteig
Pages 231-251
Year 1993
Journal J. Compl.
Volume 9
Number 2
Abstract We investigate the impact of randomization on the complexity of deciding membership in a (semi-)algebraic subset $X$ in $\mathbb R^m$. Examples are exhibited, where allowing for a certain error probability in the answer of the algorithms the complexity of decision problems decreases. A randomized decision tree over $m$ will be defined as a pair $(T,u)$ where $u$ is a probability measure on some $\mathbb R^n$ and $T$ is a decision tree over $m+n$. We prove a general lower bound on the average decision complexity for testing membership in an irreducible algebraic subset $X$ in $\mathbb R^m$ and apply it to $k$-generic complete intersection of polynomials of the same degree, extending results in Buergisser, Lickteig, and Shub (1992), and Buergisser (1992). We also give applications to nongeneric cases, such as graphs of elementary symmetric functions, $\mathrm S\mathrm L(m,\mathbb R)$, and determinant varieties, extending results in Lickteig (1990).
Link to publication Download Bibtex entry


Quick Access

Schnellnavigation zur Seite über Nummerneingabe