相关论文: Reducing Randomness via Irrational Numbers

It is common in stability analysis to linearize a system and investigate the spectrum of the Jacobian matrix. This approach faces the challenge of determining the matrix spectrum when the coefficients depend on parameters or when the…

Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low independence. A series of papers, beginning with work by Luby (1988), showed that in many cases…

Using Je\v{r}\'abek 's framework for probabilistic reasoning, we formalize the correctness of two fundamental RNC^2 algorithms for bipartite perfect matching within the theory VPV for polytime reasoning. The first algorithm is for testing…

This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…

Given a list of N numbers, the maximum can be computed in N iterations. During these N iterations, the maximum gets updated on average as many times as the Nth harmonic number. We first use this fact to approximate the Nth harmonic number…

We present a novel technique for work-efficient parallel derandomization, for algorithms that rely on the concentration of measure bounds such as Chernoff, Hoeffding, and Bernstein inequalities. Our method increases the algorithm's…

In order to verify programs or hybrid systems, one often needs to prove that certain formulas are unsatisfiable. In this paper, we consider conjunctions of polynomial inequalities over the reals. Classical algorithms for deciding these not…

In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…

This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…

A polynomial identity testing algorithm must determine whether an input polynomial (given for instance by an arithmetic circuit) is identically equal to 0. In this paper, we show that a deterministic black-box identity testing algorithm for…

A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general…

There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover…

To cater to the needs of (Zero Knowledge) proofs for (mathematical) proofs, we describe a method to transform formal sentences in 2x2-matrices over multivariate polynomials with integer coefficients, such that usual proof-steps like…

Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…

A method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points. This yields a robust and efficient method which can avoid singularities and breakdowns in the…

$ \newcommand{\ie}{i.\,e.} $We introduce a hitting set generator for Polynomial Identity Testing based on evaluations of low-degree univariate rational functions at abscissas associated with the variables. We establish an equivalence up to…

Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…

Many randomized algorithms can be derandomized efficiently using either the method of conditional expectations or probability spaces with low (almost-) independence. A series of papers, beginning with Luby (1993) and continuing with Berger…

A novel method with two variations is proposed with which the number of positive and negative zeros of a polynomial with real coefficients and degree $n$ can be restricted with significantly better determinacy than that provided by the…

For a large class of polynomials, the standard method of polynomial evaluation, Horner's method, can be very inaccurate. The alternative method given here is on average 100 to 1000 times more accurate than Horner's Method. The number of…