Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
SIAM Journal on Computing
The equivalence of two problems on the cube
Journal of Combinatorial Theory Series A
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Sensitive functions and approximate problems
Information and Computation
Sensitivity vs. block sensitivity (an average-case study)
Information Processing Letters
The Complexity of Symmetric Boolean Functions
Computation Theory and Logic, In Memory of Dieter Rödding
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On the Tightness of the Buhrman-Cleve-Wigderson Simulation
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Sensitivity versus block sensitivity of Boolean functions
Information Processing Letters
An improved lower bound on the sensitivity complexity of graph properties
Theoretical Computer Science
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
Gems in decision tree complexity revisited
ACM SIGACT News
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Sensitivity is one of the simplest, and block sensitivity one of the most useful, invariants of a boolean function. Nisan [SIAM J. Comput. 20 (6) (1991) 999] and Nisan and Szegedy [Comput. Complexity 4 (4) (1994) 301] have shown that block sensitivity is polynomially related to a number of measures of boolean function complexity. The main open question is whether or not a polynomial relationship exists between sensitivity and block sensitivity. We define the intermediate notion of l-block sensitivity, and show that, for any fixed l, this new quantity is polynomially related to sensitivity. We then achieve an improved (though still exponential) upper bound on block sensitivity in terms of sensitivity. As a corollary, we also prove that sensitivity and block sensitivity are polynomially related when the block sensitivity is Ω(n).