Related papers: Eliminating Variables in Boolean Equation Systems
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…
In this paper, we propose a new optimization framework, the layer separation (LySep) model, to improve the deep learning-based methods in solving partial differential equations. Due to the highly non-convex nature of the loss function in…
In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data…
Secure multi-party computation is an area in cryptography which studies how multiple parties can compare their private information without revealing it. Besides digital protocols, many unconventional protocols for secure multi-party…
The problem "Given a Boolean function $f$ of $n$ variables by its truth table vector. Find (if exists) a vector $\alpha \in \{0,1\}^n$ of maximal (or minimal) weight, such that $f(\alpha)= 1$." is considered here. It is closely related to…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean formulas without negations over lax polynomial inequalities. The algorithm works in weak…
In this paper, we create a systematic and automatic procedure for transforming the integer factorization problem into the problem of solving a system of Boolean equations. Surprisingly, the resulting system of Boolean equations takes on a…
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…
A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…
The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…
Research on quantum computing has recently gained significant momentum since first physical devices became available. Many quantum algorithms make use of so-called oracles that implement Boolean functions and are queried with highly…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
Recently Chen and Gao~\cite{ChenGao2017} proposed a new quantum algorithm for Boolean polynomial system solving, motivated by the cryptanalysis of some post-quantum cryptosystems. The key idea of their approach is to apply a Quantum Linear…
We propose a quantum algorithm (in the form of a quantum oracle) that estimates the closeness of a given Boolean function to one that satisfies the ``strict avalanche criterion'' (SAC). This algorithm requires $n$ queries of the Boolean…
Second order stochastic optimization methods, such as the linear method, couple the updates of different parameters and, in so doing, allow statistical uncertainty in one parameter to affect the update of other parameters. In simple tests,…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses standard arithmetic, BMF uses the Boolean OR and Boolean AND…
The Boolean circuit simplification problem involves finding a smaller circuit that computes the same function as a given Boolean circuit. This problem is closely related to several key areas with both theoretical and practical applications,…
The experimentally verified violation of Bell's inequalities apparently implies that at least one of two intuitive beliefs must be false: that effects propagating at infinite velocity do not exist, and that natural phenomena occur…
Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…