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
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Lower bounds to randomized algorithms for graph properties
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
On directional vs. undirectional randomized decision tree complexity for read-once formulas
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
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We investigate the deterministic and the randomized decision tree complexities of Boolean functions, denoted by D(f) and R(f), respectively. A long standing conjecture is that, for every Boolean function f, R(f) = Ω(D(f)α where α = log2 (1+√33/4) = 0.753... [Saks-Wigderson, FOCS '86]. In this paper, we concentrate on the class of read-once Boolean functions and propose a promising approach to attack the conjecture for this class. Precisely, we give a statement about a property of a real-valued function whose correctness implies the conjecture for all read-once Boolean functions. So far we have not succeeded to prove this statement; however, we verified by computer calculation that the statement is "at least approximately true" that implies a lower bound of R(f) = Ω(D(f)0.99α) = Ω(D(f)0.746). This improves the best known lower bound of Ω(D(f)0.51) by Heiman and Wigderson [Comput. Complexity, 1991].