On read-once threshold formulae and their randomized decision tree complexity
Theoretical Computer Science - Special issue on structure in complexity theory
Randomized Boolean decision trees: several remarks
Theoretical Computer Science - Special issue Kolmogorov complexity
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
A lower bound on the quantum query complexity of read-once functions
Journal of Computer and System Sciences
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Bounding the randomized decision tree complexity of read-once Boolean functions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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We investigate the relationship between the directional and the undirectional complexity of read-once Boolean formulas on the randomized decision tree model. It was known that there is a read-once Boolean formula such that an optimal randomized algorithm to evaluate it is not directional. This was first pointed out by Saks and Wigderson (1986) and an explicit construction of such a formula was given by Vereshchagin (1998). We conduct a systematic search for a certain class of functions and provide an explicit construction of a read-once Boolean formula f on n variables such that the cost of the optimal directional randomized decision tree for f is Ω(nα) and the cost of the optimal randomized undirectional decision tree for f is O(nβ) with α -- β 0.0101. This is the largest known gap so far.