Related papers: Fuzzy Maximum Satisfiability
In the Maximum Weight Independent Set of Rectangles problem (MWISR) we are given a weighted set of $n$ axis-parallel rectangles in the plane. The task is to find a subset of pairwise non-overlapping rectangles with the maximum possible…
We show that the linear or quadratic 0/1 program\[P:\quad\min\{ c^Tx+x^TFx : \:A\,x =b;\:x\in\{0,1\}^n\},\]can be formulated as a MAX-CUT problem whose associated graph is simply related to the matrices $\F$ and $\A^T\A$.Hence the whole…
This paper presents an algorithm for 3-SAT problems. First, logical formulas are transformed into elementary algebraic formulas. Second, complex trigonometric functions are assigned to the variables in the elementary algebraic formulas, and…
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 rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time…
As a natural variant of the $k$-SAT problem, NAE-$k$-SAT additionally requires the literals in each clause to take not-all-equal (NAE) truth values. In this paper, we study the worst-case time complexities of solving NAE-$k$-SAT and…
An improved fully polynomial-time approximation scheme and a greedy heuristic for the fractional length-bounded maximum multicommodity flow problem with unit edge-lengths are proposed. Computational experiments are carried out on benchmark…
Boolean satisfiability (SAT) problem, the first problem proven to be NP-complete, has become a fundamental challenge in computational complexity, with widespread applications in optimization and verification across many domains. Despite…
Recently a number of randomized 3/4-approximation algorithms for MAX SAT have been proposed that all work in the same way: given a fixed ordering of the variables, the algorithm makes a random assignment to each variable in sequence, in…
The quest to solve hard combinatorial optimization problems efficiently -- still a longstanding challenge for traditional digital computers -- has inspired the exploration of many alternate computing models and platforms. As a case in…
In MaxSat, we are given a CNF formula $F$ with $n$ variables and $m$ clauses and asked to find a truth assignment satisfying the maximum number of clauses. Let $r_1,..., r_m$ be the number of literals in the clauses of $F$. Then…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
We present Woorpje, a string solver for bounded word equations (i.e., equations where the length of each variable is upper bounded by a given integer). Our algorithm works by reformulating the satisfiability of bounded word equations as a…
Conflict-Driven Clause Learning (CDCL) is the mainstream framework for solving the Satisfiability problem (SAT), and CDCL solvers typically rely on various heuristics, which have a significant impact on their performance. Modern CDCL…
Random instances of constraint satisfaction problems such as k-SAT provide challenging benchmarks. If there are m constraints over n variables there is typically a large range of densities r=m/n where solutions are known to exist with…
In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN…
Modern neural networks obtain information about the problem and calculate the output solely from the input values. We argue that it is not always optimal, and the network's performance can be significantly improved by augmenting it with a…
The problem MaxLin2 can be stated as follows. We are given a system $S$ of $m$ equations in variables $x_1,...,x_n$, where each equation is $\sum_{i \in I_j}x_i = b_j$ is assigned a positive integral weight $w_j$ and $x_i,b_j \in…
Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in…
This paper formalizes the optimal base problem, presents an algorithm to solve it, and describes its application to the encoding of Pseudo-Boolean constraints to SAT. We demonstrate the impact of integrating our algorithm within the…