Related papers: Eliminating Variables in Boolean Equation Systems
Protecting source code against reverse engineering and theft is an important problem. The goal is to carry out computations using confidential algorithms on an untrusted party while ensuring confidentiality of algorithms. This problem has…
Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in…
We study the problem of detecting outlier pairs of strongly correlated variables among a collection of $n$ variables with otherwise weak pairwise correlations. After normalization, this task amounts to the geometric task where we are given…
A fundamental problem in computer science is to find all the common zeroes of $m$ quadratic polynomials in $n$ unknowns over $\mathbb{F}_2$. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity…
This paper develops upper and lower bounds for the probability of Boolean expressions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. Our technique generalizes and extends the…
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…
Boolean quadratic optimization problems occur in a number of applications. Their mixed integer-continuous nature is challenging, since it is inherently NP-hard. For this motivation, semidefinite programming relaxations (SDR's) are proposed…
This work explores the effects of relevant and irrelevant boolean variables on the accuracy of classifiers. The analysis uses the assumption that the variables are conditionally independent given the class, and focuses on a natural family…
Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the constraint over an auxiliary matrix whose Boolean structure…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
The growing size of modern datasets necessitates splitting a large scale computation into smaller computations and operate in a distributed manner. Adversaries in a distributed system deliberately send erroneous data in order to affect the…
We propose a method of optimizing monotone Boolean circuits by re-writing them in a simpler, equivalent form. We use in total six heuristics: Hill Climbing, Simulated Annealing, and variations of them, which operate on the representation of…
We study systems of String Equations where block variables need to be assigned strings so that their concatenation gives a specified target string. We investigate this problem under a multivariate complexity framework, searching for…
The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh coefficients of an $n$ variable Boolean function. Roughly speaking, it takes a…
We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In…
We aim to advance the state-of-the-art in Quadratic Unconstrained Binary Optimization formulation with a focus on cryptography algorithms. As the minimal QUBO encoding of the linear constraints of optimization problems emerges as the…
Bayesian optimization (BO) methods are useful for optimizing functions that are expensive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…