Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
A Discrete Approximation and Communication Complexity Approach to the Superposition Problem
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Distributed Algorithmic Mechanism Design and Algebraic Communication Complexity
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Probabilistic Communication Complexity Over The Reals
Computational Complexity
Hilbert's Thirteenth Problem and Circuit Complexity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Using kolmogorov inspired gates for low power nanoelectronics
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
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In function theory the superposition problem is known as the problem of representing a continuous function f(x1, … ,xk) in k variables as the composition of “simpler” functions. This problem stems from the Hilbert's thirteenth problem. In computer science good formalization for the notion of composition of functions is formula. In the paper we consider real-valued continuous functions in k variables in the cube [0,1]k from the class ℋk&ohgr;p with &ohgr;p a special modulus of continuity (measure the smoothness of a function) defined in the paper. ℋk&ohgr;p is a superset of Hölder class of functions. We present an explicit function f ∈ ℋk&ohgr;p which is hard in the sense that it cannot be represented in the following way as a formula: zero level (input) gates associated with variables {x1, … ,xk} (different input gates can be associated with the same variable xi ∈ {x1, … ,xk}), on the first level of the formula, arbitrary number s ≥ 1 of t variable functions from ℋt&ohgr;p for t