Related papers: Representing Boolean Functions Using Polynomials: …
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying…
It is known a method for converting a system of Boolean polynomial equations to a single Boolean polynomial equation with less variables. In this paper, we show a formula for systems of Boolean polynomial equations which is based on the…
We show that sharp thresholds for Boolean functions directly imply average-case circuit lower bounds. More formally we show that any Boolean function exhibiting a sharp enough threshold at \emph{arbitrary} critical density cannot be…
Boolean functions are important primitives in different domains of cryptology, complexity and coding theory. In this paper, we connect the tools from cryptology and complexity theory in the domain of Boolean functions with low polynomial…
In this paper, we present a generic parametrization of generically zero-dimensional parametric polynomial systems. More specifically, we study the specialization properties of the Rational Univariate Representation and derive bounds on the…
We study the approximation capabilities of two families of univariate polynomials that arise in applications of quantum signal processing. Although approximation only in the domain $[0,1]$ is physically desired, these polynomial families…
A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean literals. One of the popular, efficient ideas used to solve PB-problems (a set of PB-constraints) is to translate them to SAT instances (encodings) via, for…
Boolean functions with high algebraic immunity are important cryptographic primitives in some stream ciphers. In this paper, two methodologies for constructing binary minimal codes from sets, Boolean functions and vectorial Boolean…
Recently classes of conic and discrete conic functions were introduced. In this paper we use the term convic instead conic. The class of convic functions properly includes the classes of convex functions, strictly quasiconvex functions and…
One of the major issues of cryptography is the cryptanalysis of cipher algorithms. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required.…
We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…
A polynomial identity testing algorithm must determine whether a given input polynomial is identically equal to 0. We give a deterministic black-box identity testing algorithm for univariate polynomials of the form $\sum_{j=0}^t c_j…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the…
A polynomial transform is the multiplication of an input vector $x\in\C^n$ by a matrix $\PT_{b,\alpha}\in\C^{n\times n},$ whose $(k,\ell)$-th element is defined as $p_\ell(\alpha_k)$ for polynomials $p_\ell(x)\in\C[x]$ from a list…
In this paper we consider the computational complexity of the following problem. Let $f$ be a Boolean polynomial. What value of $f$, 0 or 1, is taken more frequently? The problem is solved in polynomial time for polynomials of degrees 1,2.…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…