Details:
Title  On the intrinsic complexity of elimination theory  Author(s)  Joos Heintz, Jacques Morgenstern  Type  Article in Journal  Abstract  We consider the intrinsic complexity of selected algorithmic problems of classical elimination theory in algebraic geometry. The inputs and outputs of these problems are given by finite sets of polynomials which we represent alternatively in dense form or by straight line programs. We begin with an overview on the known upper bounds for the sequential and parallel time complexity of these problems and show then that in the most important cases these bounds are tight. Our lower bound results include both the relative and the absolute viewpoint of complexity theory. On one side we give reductions of fundamental questions of elimination theory to NP and P#complete problems and on the other side we show that some of these questions may have exponential size outputs. In this way we confirm the intrinsically exponential character of algorithmic problems in elimination theory whatever the type of data structure may be.  ISSN  0885064X 
URL 
dx.doi.org/10.1006/jcom.1993.1031 
Language  English  Journal  Journal of Complexity  Volume  9  Number  4  Pages  471498  Publisher  Academic Press, Inc.  Address  Orlando, FL, USA  Year  1993  Month  December  Translation 
No  Refereed 
No 
