Lower bounds for algebraic computation trees

Michael Ben-Or
1983 Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83  
A topological method is given for obtaining lower bounds for the height of algebraic computation trees, and algebraic decision trees. Using this method we are able to generalize, and present in a uniform and easy way, almost all the known nonlinear lower bounds for algebraic computations. Applying the method to decision trees we extend all the apparently known lower bounds for linear decision trees to bounded degree algebraic decision trees, thus answering the open questions raised by Steele
more » ... Yao [20] . We also show how this new method can be used to establish lower bounds on the complexity of constructions with ruler and compass in plane Euclidean geometry.
doi:10.1145/800061.808735 dblp:conf/stoc/Ben-Or83 fatcat:lwhhw5siejedjagvnnvadm2oeq