Related papers: Numerical Solution-Space Analysis of Satisfiabilit…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
A kernelization algorithm for a computational problem is a procedure which compresses an instance into an equivalent instance whose size is bounded with respect to a complexity parameter. For the Boolean satisfiability problem (SAT), and…
Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…
The rigorous theoretical analyses of algorithms for exact 3-satisfiability (X3SAT) have been proposed in the literature. As we know, previous algorithms for solving X3SAT have been analyzed only regarding the number of variables as the…
The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side, especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT…
We present algorithms based on satisfiability problem (SAT) solving, as well as answer set programming (ASP), for solving the problem of determining inconsistency degrees in propositional knowledge bases. We consider six different…
Efficient solutions to NP-complete problems would significantly benefit both science and industry. However, such problems are intractable on digital computers based on the von Neumann architecture, thus creating the need for alternative…
Boolean satisfiability (SAT) solvers are widely used in hardware verification, cryptanalysis, automatic test-pattern generation, and side-channel reasoning workflows. Modern conflict-driven clause-learning (CDCL) solvers are highly…
In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…
Three algorithms are presented that determine the existence of satisfying assignments for 3SAT Boolean satisfiability expressions. One algorithm is presented for determining an instance of a satisfying assignment, where such exists. The…
The Local Search algorithm (or Hill Climbing, or Iterative Improvement) is one of the simplest heuristics to solve the Satisfiability and Max-Satisfiability problems. It is a part of many satisfiability and max-satisfiability solvers, where…
Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…
It has been shown that Maximum Satisfiability (MaxSAT) problem instances can be effectively solved by partitioning the set of soft clauses into several disjoint sets. The partitioning methods can be based on clause weights (e.g.,…
The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground…
This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…
The NeuroSAT neural network architecture was recently introduced for predicting properties of propositional formulae. When trained to predict the satisfiability of toy problems, it was shown to find solutions and unsatisfiable cores on its…
During the past decade, phase-transition phenomena in the random 3-satisfiability (3-SAT) problem has been intensively studied by statistical physics methods. In this work, we study the random 3-SAT problem by the mean-field first-step…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…