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A d-dimensional framework is a graph and a map from its vertices to E d. Such a framework is globally rigid if it is the only framework in E d with the same graph and edge lengths, up to rigid motions. For which underlying graphs is a generic framework globally rigid? We answer this question by proving a conjecture by Connelly, that his sufficient condition… (More)

We introduce a new flavor of commitment schemes, which we call mercurial commitments. Informally, mercurial commitments are standard commitments that have been extended to allow for soft decommitment. Soft decommitments, on the one hand, are not binding but, on the other hand, cannot be in conflict with true decommitments. We then demonstrate that a… (More)

In response to the current financial crisis, a number of hedge funds have implemented " gates " on their funds that restrict withdrawals when the sum of redemption requests exceeds a certain percentage of the fund's total assets. To reduce the investor's risk exposures during these periods, we propose a futures overlay strategy designed to hedge out or… (More)

We revisit the problem of hardness amplification in NP, as recently studied by O'Donnell (STOC '02). We prove that if NP has a balanced function <i>f</i> such that any circuit of size <i>s</i>(<i>n</i>) fails to compute <i>f</i> on a 1/poly(<i>n</i>) fraction of inputs, then NP has a function <i>f</i>′ such that any circuit of size… (More)

We study the complexity of arithmetic in finite fields of characteristic two, F 2 n. We concentrate on the following two problems: First, we consider the explicit realization of the field F 2 n as F 2 [x]/(x 2·3 l +x 3 l +1) F 2 n , where n = 2·3 l. In this setting, we exhibit Dlogtime-uniform poly(n, t)-size T C 0 circuits computing exponentiation. To the… (More)

We develop a general approach for improving the efficiency of a computationally bounded receiver interacting with a powerful and possibly malicious sender. The key idea we use is that of delegating some of the receiver's computation to the (potentially malicious) sender. This idea was recently introduced by Goldwasser et al. [14] in the area of program… (More)

Program checking, program self-correcting and program self-testing were pioneered by [Blum and Kannan] and [Blum, Luby and Rubinfeld] in the mid eighties as a new way to gain confidence in software, by considering program correctness on an input by input basis rather than full program verification. Work in the field of program checking focused on designing,… (More)

- Alexander Healy
- 2006

We construct a randomness-efficient averaging sampler that is computable by uniform constant-depth circuits with parity gates (i.e., in uniform AC 0 [⊕]). Our sampler matches the parameters achieved by random walks on constant-degree expander graphs, allowing us to apply a variety expander-based techniques within NC 1. For example, we obtain the following… (More)

We will develop the machinery of resultants and resolvent polynomials with the ultimate goal of understanding the so-called " resolvent method " for computing Galois groups over Q. Along the way, we will encounter tangential applications of these tools, such as the determination of the minimal polynomial of, say, the sum of two algebraic numbers using… (More)