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On Lower Bounds for Algebraic Decision Trees over the Complex Numbers
2010
2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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We prove a new lower bound for the decision complexity of a complex algebraic set X in terms of the sum of its (compactly supported) Betti numbers b c (X), which is for the first time better than logarithmic in b c (X). We apply this result to subspace arrangements including some well studied problems such as the knapsack and element distinctness problems.
doi:10.1109/synasc.2010.73
dblp:conf/synasc/Scheiblechner10
fatcat:6ohlnzhapjdkpmifq4cfne75dy