Related papers: A Polynomial Time Algorithm for 3-SAT

Limits on the number of satisfying assignments for CNS instances with n variables and m clauses are derived from various inequalities. Some bounds can be calculated in polynomial time, sharper bounds demand information about the…

In this paper, we propose an algorithm for the positive one-in-three satisfiability problem (Pos1in3SAT). The proposed algorithm can efficiently decide the existence of a satisfying assignment in all assignments for a given formula by using…

The Deutsch model of quantum computation is extended to allow for thermodynamically irreversible operations by allowing the system of interest to interact with an outside reservoir. A set of irreversible logical error correction…

The classical work of (Arora et al., 1999) provides a scheme that gives, for any $\epsilon>0$, a polynomial time $1-\epsilon$ approximation algorithm for dense instances of a family of $\mathcal{NP}$-hard problems, such as Max-CUT and…

We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…

The importance of algorithm portfolio techniques for SAT has long been noted, and a number of very successful systems have been devised, including the most successful one --- SATzilla. However, all these systems are quite complex (to…

Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance…

This work solves 3SAT, a classical NP-complete problem, on a CMOS-based Ising hardware chip with all-to-all connectivity. The paper addresses practical issues in going from algorithms to hardware. It considers several degrees of freedom 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…

In the last decades, many efforts have focused on analyzing typical-case hardness in optimization and inference problems. Some recent work has pointed out that polynomial algorithms exist, running with a time that grows more than linearly…

The method in this paper is wrong.

There is a number of known NP class problems, and majority of them have been shown to be equivalent to others. In particular now it is clear that construction of a Gr\"{o}bner basis (or Buchberger algorithm) must be one of equivalent…

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.…

The aim of the paper is to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard…

SARRIGUREN, a new complete algorithm for SAT based on counting clauses (which is valid also for Unique-SAT and #SAT) is described, analyzed and tested. Although existing complete algorithms for SAT perform slower with clauses with many…

Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…

To check the satisfiability of (non-linear) real arithmetic formulas, modern satisfiability modulo theories (SMT) solving algorithms like NLSAT depend heavily on single cell construction, the task of generalizing a sample point to a…

While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…

In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…

A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…