In this paper we study the computational complexity of computing the noncommutative determinant. We first consider the arithmetic circuit complexity of computing the noncommutativ...
We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(log(nD(f))) iterations (grid refinements) where n is...
Felipe Cucker, Teresa Krick, Gregorio Malajovich, ...
We develop a theory of online learning by defining several complexity measures. Among them are analogues of Rademacher complexity, covering numbers and fatshattering dimension fro...
Alexander Rakhlin, Karthik Sridharan, Ambuj Tewari
The Vapnik-Chervonenkis (V-C) dimension is an important combinatorial tool in the analysis of learning problems in the PAC framework. For polynomial learnability, we seek upper bou...
We address the non-redundant random generation of k words of length n from a context-free language. Additionally, we want to avoid a predefined set of words. We study the limits of...