Related papers: Boolean Equi-propagation for Concise and Efficient…
Bayesian optimization is a powerful optimization tool for problems where native first-order derivatives are unavailable. Recently, constrained Bayesian optimization (CBO) has been applied to many engineering applications where constraints…
In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over…
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
Recent progress in Generative Artificial Intelligence (AI) relies on efficient data representations, often featuring encoder-decoder architectures. We formalize the mathematical problem of finding the optimal encoder-decoder pair and…
We present a simple randomized algorithm that approximates the number of satisfying assignments of Boolean formulas in conjunctive normal form. To the best of our knowledge this is the first algorithm which approximates #k-SAT for any k >=…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely…
In this work we revisit the Boolean Hidden Matching communication problem, which was the first communication problem in the one-way model to demonstrate an exponential classical-quantum communication separation. In this problem, Alice's…
The quantum approximate optimization algorithm is commonly used to solve combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint…
As Cook-Levin theorem showed, every NP problem can be reduced to SAT in polynomial time. In this paper I show a simpler and more efficent method to reduce some factorization problems to the satisfability of a boolean formula.
Unit propagation (which is called also Boolean Constraint Propagation) has been an important component of every modern CDCL SAT solver since the CDCL solver was developed. In general, unit propagation is implemented by scanning sequentially…
Graph generation and enumeration problems often require handling equivalent graphs -- those that differ only in vertex labeling. We study how to extend SAT Modulo Symmetries (SMS), a framework for eliminating such redundant graphs, to…
The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more…
The quantified Boolean formula problem (QBF) is a well-known PSpace-complete problem with rich expressive power, and is generally viewed as the SAT analogue for PSpace. Given that many problems today are solved in practice by reducing to…
Algebraic Normal Form (ANF) and Conjunctive Normal Form (CNF) are commonly used to encode problems in Boolean algebra. ANFs are typically solved via Gr"obner basis algorithms, often using more memory than is feasible; while CNFs are solved…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the…
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…