We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost line...
Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomial-time samplable distribution (e.g., the uniform distribution) and...
We show that if an NP-complete problem has a non-adaptive self-corrector with respect to a samplable distribution then coNP is contained in NP/poly and the polynomial hierarchy co...
We study multivariate approximation for continuous functions in the average case setting. The space of d variate continuous functions is equipped with the zero mean Gaussian measu...
Abstract. We advocate to analyze the average complexity of learning problems. An appropriate framework for this purpose is introduced. Based on it we consider the problem of learni...