Probabilistic communication complexity
Journal of Computer and System Sciences
Meanders and their applications in lower bounds arguments
Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Different modes of communication
SIAM Journal on Computing
Threshold circuits of bounded depth
Journal of Computer and System Sciences
On the computational power of depth 2 circuits with threshold and modulo gates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Geometric arguments yield better bounds for threshold circuits and distributed computing
Theoretical Computer Science
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
An Algorithmic Theory of Learning: Robust Concepts and Random Projection
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Linear Lower Bound on the Unbounded Error Probabilistic Communication Complexity
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Geometrical realization of set systems and probabilistic communication complexity
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Polynomial threshold functions, AC functions and spectrum norms
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
On the size of randomized OBDDs and read-once branching programs for k-stable functions
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the Representation of Boolean Predicates of the Diffie-Hellman Function
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
ALT '02 Proceedings of the 13th International Conference on Algorithmic Learning Theory
Threshold circuit lower bounds on cryptographic functions
Journal of Computer and System Sciences
SIAM Journal on Computing
Lower bounds for linear decision trees via an energy complexity argument
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Bounded Independence Fools Halfspaces
SIAM Journal on Computing
Spectral norm in learning theory: some selected topics
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
On the complexity of depth-2 circuits with threshold gates
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Unbounded-error one-way classical and quantum communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Hi-index | 0.00 |
Recently, Forster [7] proved a new lower bound on probabilistic communication complexity in terms of the operator norm of the communication matrix. In this paper, we want to exploit the various relations between communication complexity of distributed Boolean functions, geometric questions related to half space representations of these functions, and the computational complexity of these functions in various restricted models of computation. In order to widen the range of applicability of Forster's bound, we start with the derivation of a generalized lower bound. We present a concrete family of distributed Boolean functions where the generalized bound leads to a linear lower bound on the probabilistic communication complexity (and thus to an exponential lower bound on the number of Euclidean dimensions needed for a successful half space representation), whereas the old bound fails. We move on to a geometric characterization of the well known communication complexity class C-PP in terms of half space representations achieving a large margin. Our characterization hints to a close connection between the bounded error model of probabilistic communication complexity and the area of large margin classification. In the final section of the paper, we describe how our techniques can be used to prove exponential lower bounds on the size of depth-2 threshold circuits (with still some technical restrictions). Similar results can be obtained for read-k-times randomized ordered binary decision diagram and related models.