scholarly journals NLocalSAT: Boosting Local Search with Solution Prediction

2020 ◽  
Author(s):  
Wenjie Zhang ◽  
Zeyu Sun ◽  
Qihao Zhu ◽  
Ge Li ◽  
Shaowei Cai ◽  
...  
Keyword(s):  
Neural Network ◽  
Local Search ◽  
Prediction Model ◽  
Computer Science ◽  
Boolean Satisfiability ◽  
Stochastic Local Search ◽  
Boolean Satisfiability Problem ◽  
Complete Problem ◽  
Random Manner ◽  
Np Complete

The Boolean satisfiability problem (SAT) is a famous NP-complete problem in computer science. An effective way for solving a satisfiable SAT problem is the stochastic local search (SLS). However, in this method, the initialization is assigned in a random manner, which impacts the effectiveness of SLS solvers. To address this problem, we propose NLocalSAT. NLocalSAT combines SLS with a solution prediction model, which boosts SLS by changing initialization assignments with a neural network. We evaluated NLocalSAT on five SLS solvers (CCAnr, Sparrow, CPSparrow, YalSAT, and probSAT) with instances in the random track of SAT Competition 2018. The experimental results show that solvers with NLocalSAT achieve 27% ~ 62% improvement over the original SLS solvers.

scholarly journals The Computational Complexity of Probabilistic Planning

1998 ◽  
Vol 9 ◽  
pp. 1-36 ◽  
Author(s):  
M. L. Littman ◽  
J. Goldsmith ◽  
M. Mundhenk
Keyword(s):  
Computational Complexity ◽  
Efficient Algorithms ◽  
Boolean Satisfiability ◽  
Complexity Classes ◽  
Probabilistic Planning ◽  
Plan Evaluation ◽  
Partially Ordered ◽  
Boolean Satisfiability Problem ◽  
Complete Problem ◽  
Planning Problems

We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, co-NP, PP, NP^PP, co-NP^PP, and PSPACE. In the process of proving that certain planning problems are complete for NP^PP, we introduce a new basic NP^PP-complete problem, E-MAJSAT, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for E-MAJSAT could be important for the creation of efficient algorithms for a wide variety of problems.

scholarly journals Applying Neural Networks to Find the Minimum Cost Coverage of a Boolean Function

VLSI Design ◽  
1995 ◽  
Vol 3 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Pong P. Chu
Keyword(s):  
Neural Network ◽  
Boolean Function ◽  
Input Data ◽  
Selection Process ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Hopfield Network ◽  
Neural Network Approach ◽  
Complete Problem ◽  
Np Complete

To find a minimal expression of a boolean function includes a step to select the minimum cost cover from a set of implicants. Since the selection process is an NP-complete problem, to find an optimal solution is impractical for large input data size. Neural network approach is used to solve this problem. We first formalize the problem, and then define an “energy function” and map it to a modified Hopfield network, which will automatically search for the minima. Simulation of simple examples shows the proposed neural network can obtain good solutions most of the time.

An Efficient Technique to Ensure the Logical Consistency of Interacting Knowledge Bases

1997 ◽  
Vol 06 (01) ◽  
pp. 27-36 ◽  
Author(s):  
Bertrand Mazure ◽  
Lakhdar Saïs ◽  
Éric Grégoire
Keyword(s):  
Local Search ◽  
Fundamental Problem ◽  
Real Life ◽  
Knowledge Bases ◽  
The Other ◽  
Logical Consistency ◽  
Complete Problem ◽  
Np Complete ◽  
The One ◽  
Cooperative Knowledge

In this paper, we address a fundamental problem in the formalization and implementation of cooperative knowledge bases: the difficulty of preserving consistency while interacting or combining them. Indeed, knowledge bases that are individually consistent can exhibit global inconsistency. This stumbling-block problem is an even more serious drawback when knowledge and reasoning are expressed using logical terms. Indeed, on the one hand, two contradictory pieces of information lead to global inconsistency under complete standard rules of deduction: every assertion and its contrary can be deduced. On the other hand, checking the logical consistency of a propositional knowledge base is an NP-complete problem and is often out of reach for large real-life applications. In this paper, a new practical technique to locate inconsistent interacting pieces of information is presented in the context of cooperative logical knowledge bases. Based on a recently discovered heuristic about the work performed by local search techniques, it can be applied in the context of large interacting knowledge bases.

scholarly journals Polynomial time solution to NP-complete problem Hamiltonian cycle (P=NP Proof)

2021 ◽  
Author(s):  
Yasaman KalantarMotamedi
Keyword(s):  
Computer Science ◽  
Polynomial Time ◽  
Hamiltonian Cycle ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Rigorous Proof ◽  
Complete Problem ◽  
Time Solution ◽  
Np Complete

P vs NP is one of the open and most important mathematics/computer science questions that has not been answered since it was raised in 1971 despite its importance and a quest for a solution since 2000. P vs NP is a class of problems that no polynomial time algorithm exists for any. If any of the problems in the class gets solved in polynomial time, all can be solved as the problems are translatable to each other. One of the famous problems of this kind is Hamiltonian cycle. Here we propose a polynomial time algorithm with rigorous proof that it always finds a solution if there exists one. It is expected that this solution would address all problems in the class and have a major impact in diverse fields including computer science, engineering, biology, and cryptography.

Deformation Monitoring Model of Jinping-I Hydropower Station Based on NACA-BP Neural Network

2014 ◽  
Vol 704 ◽  
pp. 257-260
Author(s):  
De Wen Cai ◽  
Chen Fei Shao ◽  
Di Kai Wang ◽  
Er Feng Zhao ◽  
Meng Yang
Keyword(s):  
Neural Network ◽  
Local Search ◽  
Prediction Model ◽  
Bp Neural Network ◽  
Ant Colony Algorithm ◽  
Back Propagation ◽  
Deformation Monitoring ◽  
Ant Colony ◽  
Monitoring Data ◽  
Neural Network Modeling

Back Propagation (BP) neural network can learn and store a large number of input-output model nonlinear relationships with simple structure. Niche ant colony algorithm (NACA) combines the ant colony algorithm (ACA) with the niche technology in order to add its local search ability to ACA with preserving the intelligent search ability and robustness of ACA. To optimize predicting model establishment of the dam monitoring data, NACA and BP neural network modeling method are combined to establish a prediction model of horizontal displacement monitoring data. The traditional BP neural network prediction model is established to make a comparison with the NACA. The results show that NACA-BP neural network method can speed up the convergence rate of BP neural network and enhance local search ability and prediction accuracy.

AN ANNEALED CHAOTIC MAXIMUM NEURAL NETWORK FOR BIPARTITE SUBGRAPH PROBLEM

2004 ◽  
Vol 14 (02) ◽  
pp. 107-116 ◽  
Author(s):  
JIAHAI WANG ◽  
ZHENG TANG ◽  
RONGLONG WANG
Keyword(s):  
Neural Network ◽  
Parallel Algorithm ◽  
Chaotic Dynamics ◽  
Neural Model ◽  
Steepest Descent Method ◽  
Stable Equilibrium Point ◽  
Local Minima ◽  
Complete Problem ◽  
Bipartite Subgraph ◽  
Np Complete

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP–complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP–complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.

Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings

2006 ◽  
Vol 35 (1-3) ◽  
pp. 143-179 ◽  
Author(s):  
Alan M. Frisch ◽  
Timothy J. Peugniez ◽  
Anthony J. Doggett ◽  
Peter W. Nightingale
Keyword(s):  
Local Search ◽  
Boolean Satisfiability ◽  
Stochastic Local Search ◽  
Satisfiability Problems

FRACTAL STRUCTURE ON k-SAT

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 227-232 ◽  
Author(s):  
QIN WANG ◽  
LIFENG XI
Keyword(s):  
Hausdorff Dimension ◽  
Euclidean Space ◽  
Computer Science ◽  
Fractal Structure ◽  
Reasonable Condition ◽  
Complete Problem ◽  
Np Complete ◽  
Boolean Expressions

The k-SAT (k ≥ 3) is a typical NP-complete problem in computer science. To visualize k-SAT, we embed the Boolean expressions in k-CNF, with variables in an infinite list, into cube [0, 1]k of Euclidean space. In this paper, we find fractal structure of the visualized image of satisfiable expressions, we also prove that the image has full Hausdorff dimension k under some reasonable condition, by constructing some Moran subset. The results show this image is quite different from that with respect to a finite list of Boolean variables as in Refs. 1 and 2.

Collective Adaptation: The Exchange of Coding Segments

1998 ◽  
Vol 6 (4) ◽  
pp. 311-338 ◽  
Author(s):  
Thomas Haynes
Keyword(s):  
Local Search ◽  
Collective Memory ◽  
Search Heuristic ◽  
Fitness Evaluation ◽  
Complete Problem ◽  
Search Heuristics ◽  
Np Complete

Coding segments are those subsegments of the chromosome that contribute positively to the fitness evaluation of the chromosome. Clique detection is a NP-complete problem in which we can detect such coding segments. We extract coding segments from chromosomes, and we investigate the duplication of coding segments inside the chromosome and the collection of coding segments outside of the chromosome. We find that duplication of coding segments inside the chromosomes provides a back-up mechanism for the search heuristics. We further find local search in a collective memory of coding segments outside of the chromosome, collective adaptation, enables the search heuristic to represent partial solutions that are larger than realistic chromosomes lengths and to express the solution outside of the chromosome.

Solving Non-Boolean Satisfiability Problems with Stochastic Local Search: A Comparison of Encodings

SAT 2005 ◽  
2007 ◽  
pp. 143-179 ◽  
Author(s):  
Alan M. Frisch ◽  
Timothy J. Peugniez ◽  
Anthony J. Doggett ◽  
Peter W. Nightingale
Keyword(s):  
Local Search ◽  
Boolean Satisfiability ◽  
Stochastic Local Search ◽  
Satisfiability Problems
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