The complexity of problems on probabilistic, nondeterministic, and alternating decision trees
Journal of the ACM (JACM)
Lower bounds for solving linear diophantine equations on random access machines
Journal of the ACM (JACM)
Simulating probabilistic by deterministic algebraic computation trees
Theoretical Computer Science
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Linear decision trees: volume estimates and topological bounds
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On randomized semi-algebraic test complexity
Journal of Complexity
Point location in arrangements of hyperplanes
Information and Computation
A randomized algorithm for finding maximum with O((log n)2) polynomial tests
Information Processing Letters
Decision tree complexity and Betti numbers
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On real Turing machines that toss coins
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Randomized Ω(n2) lower bound for knapsack
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Randomized complexity lower bounds
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On separating the read-k-times branching program hierarchy
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Lower bounds for high dimensional nearest neighbor search and related problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An exponential lower bound on the size of algebraic decision trees for max
Computational Complexity
A Lower Bound to Finding Convex Hulls
Journal of the ACM (JACM)
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On the Complexity of Genuinely Polynomial Computation
MFCS '90 Proceedings of the Mathematical Foundations of Computer Science 1990
Randomness, Provability, and the Seperation of Monte Carlo Time and Space
Computation Theory and Logic, In Memory of Dieter Rödding
Lower Time Bounds for Randomized Computation
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Time Space Tradeoffs (Getting Closer to the Barrier?)
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Lower Bounds for Deterministic and Nondeterministic Branching Programs
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Lower bounds for algebraic computation trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Lower Bound for Randomized Linear Decision Trees Recognising a Union of Hyperplanes in a Generic Position
Nondeterministic versus probabilistic linear search algorithms
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Algebraic decision trees and Euler characteristics
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Proving simultaneous positivity of linear forms
Journal of Computer and System Sciences
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We survey some of the recent results on the complexity of recognizing n-dimensional linear arrangements and convex polyhedra by randomized algebraic decision trees. We give also a number of concrete applications of these results. In particular, we derive first nontrivial, in fact quadratic, randomized lower bounds on the problems like Knapsack and Bounded Integer Programming. We formulate further several open problems and possible directions for future research.