Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Communication complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exponential separation of quantum and classical communication complexity
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Towards proving strong direct product theorems
Computational Complexity
Separating AC0 from depth-2 majority circuits
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A Direct Product Theorem for Discrepancy
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Complexity measures of sign matrices
Combinatorica
Lattices, mobius functions and communications complexity
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
The Unbounded-Error Communication Complexity of Symmetric Functions
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Learning complexity vs communication complexity
Combinatorics, Probability and Computing
Lower bounds in communication complexity based on factorization norms
Random Structures & Algorithms
On the Tightness of the Buhrman-Cleve-Wigderson Simulation
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Multiparty Communication Complexity and Threshold Circuit Size of AC^0
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Lower Bounds in Communication Complexity
Lower Bounds in Communication Complexity
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
Communication complexities of symmetric XOR functions
Quantum Information & Computation
Quantum communication complexity of block-composed functions
Quantum Information & Computation
Circuits, communication and polynomials
Circuits, communication and polynomials
SIAM Journal on Computing
Tight bounds on communication complexity of symmetric XOR functions in one-way and SMP models
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
The NOF multiparty communication complexity of composed functions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
A well-studied class of functions in communication complexity are composed functions of the form (f o gn)(x, y) = f(g(x1, y1),..., g(xn, yn)). This is a rich family of functions which encompasses many of the important examples in the literature. It is thus of great interest to understand what properties of f and g affect the communication complexity of (f o gn), and in what way. Recently, Sherstov [She09] and independently Shi-Zhu [SZ09b] developed conditions on the inner function g which imply that the quantum communication complexity of f o gn is at least the approximate polynomial degree of f. We generalize both of these frameworks. We show that the pattern matrix framework of Sherstov works whenever the inner function g is strongly balanced--we say that g : X × Y → {-1, +1} is strongly balanced if all rows and columns in the matrix Mg = [g(x, y)]x,y sum to zero. This result strictly generalizes the pattern matrix framework of Sherstov [She09], which has been a very useful idea in a variety of settings [She08b, RS08, Cha07, LS09a, CA08, BHN09]. Shi-Zhu require that the inner function g has small spectral discrepancy, a somewhat awkward condition to verify. We relax this to the usual notion of discrepancy. We also enhance the framework of composed functions studied so far by considering functions F(x, y) = f(g(x, y)), where the range of g is a group G. When G is Abelian, the analogue of the strongly balanced condition becomes a simple group invariance property of g. We are able to formulate a general lower bound on F whenever g satisfies this property.