Time-space tradeoffs for some algebraic problems

Authors:
Joseph Ja'Ja'
Affiliations:
-
Venue:
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Year:
1980

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Abstract

We study the time-space relationship of several algebraic problems such as matrix multiplication and matrix inversion. Several results relating the algebraic properties of a set of functions to the structure of the graph of any straight-line program, that computes this set, are shown. Some of our results are the following. Multiplying m × n by n × p matrices with space S requires at least time T ≥ &Ohgr;(mnp/S). Inverting an n × n matrix with space S requires at least time T ≥ &Ohgr;(n4/S).