Abstract
In recent years, concepts from group theory have played an important role in the derivation of lower bounds for computational complexity. In this talk we present two new results in algebraic complexity obtained with group-theoretical arguments. We show that any algebraic computation tree for the membership question of a compact set S in R n must have height Ω(log(β i(S)))−cn for all i, where β i are the Betti numbers. We also show that, to compute the sum of n independent radicals using logarithms, exponentiations and root-takings, at least n operations are required. (The second result was obtained jointly with Dima Grigoriev and Mike Singer.) This talk will be self-contained.
This work was supported in part by NSF Grant CCR-9301430.
This is a preview of subscription content, log in via an institution.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yao, A.C. (1993). Groups and algebraic complexity. In: Dehne, F., Sack, JR., Santoro, N., Whitesides, S. (eds) Algorithms and Data Structures. WADS 1993. Lecture Notes in Computer Science, vol 709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57155-8_233
Download citation
DOI: https://doi.org/10.1007/3-540-57155-8_233
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57155-1
Online ISBN: 978-3-540-47918-5
eBook Packages: Springer Book Archive