Garg, Jain, and Sahai first consider zero knowledge proofs in the presence of leakage on the local state of the prover, and present a leakageresilient-zero-knowledge proof system for HC (Hamiltonian Cycle) problem. Their construction is called (1 + ε)-leakage-resilient zero-knowledge, for any constant ε > 0, because the total length of the leakage the simulator needs is (1 + ε) times as large a...

BACKGROUND The main focus of studies of individuals at ultra-high risk for psychosis (UHR) has been on identifying brain changes in those individuals who will develop psychosis. However, longitudinal studies have shown that up to half of UHR individuals are resilient, with symptomatic remission and good functioning at follow-up. Yet little is known about brain development in resilient individua...

1 In this paper we derive several important results towards a better understanding of propagation characteristics of resilient Boolean functions. We first introduce a new upper bound on nonlinearity of a given resilient function depending on the propagation criterion. We later show that a large class of resilient functions admit a linear structure; more generally, we exhibit some divisibility p...

We analyze the performance of resilient functions for imperfect input bits. Specifically, we allow more input bits than the resiliency degree of the resilient function to be biased and analyze the output behavior under this new assumption. We develop bounds on the output distribution of resilient functions build from a number of families of linear codes. We develop an explicit formula for the p...

Wr rxttnd the notions of correlation-immune functions and resilient functions to functions over any finite alphabet endowed with the structure of an Abelian group. Thus we generalize the results of Gopalakrishnan and Slinsori as wc givc an orthogonal array characterizat,ion and a Fourier transform characterization for resilient functions over any finite alphabet. This leads to a generalization ...

In this paper, the delay-dependent robust resilient H∞ control is investigated for singular time-delay systems with norm-bounded parameter uncertainty. First, a new delaydependent bounded real lemma (BRL) for the nominal singular time-delay system is established. Then the problem of robust resilient H∞ control is solved via a resilient controller with respect to additive and multiplicative cont...

In the faulty-memory RAM model, the content of memory cells can get corrupted at any time during the execution of an algorithm, and a constant number of uncorruptible registers are available. A resilient data structure in this model works correctly on the set of uncorrupted values. In this paper we introduce a resilient priority queue. The deletemin operation of a resilient priority queue retur...

The hypothesis that different brands and models of manufactured resilient channels have significantly different acoustical performance is common in North America. Additionally, there is ample evidence that improper installation reduces the performance of resilient channel assemblies. However, many of the differences in acoustical performance associated with brand and/or installation of resilien...

A function f is d-resilient if all its Fourier coefficients of degree at most d are zero, i.e. f is uncorrelated with all low-degree parities. We study the notion of approximate resilience of Boolean functions, where we say that f is α-approximately d-resilient if f is α-close to a [−1, 1]-valued d-resilient function in `1 distance. We show that approximate resilience essentially characterizes ...