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A Preliminary Investigation of Satisfiability Problems Not Harder Than 1-In-3-SAT

Victor Lagerkvist, Biman Roy
In this paper we are interested in classifying the NP-complete SAT(Γ) problems whose worst-case time complexity is lower than 1-in-3-SAT but higher than the easiest problem SAT(R = = =01 1/3).  ...  The parameterized satisfiability problem over a set of Boolean relations Γ (SAT(Γ)) is the problem of determining whether a conjunctive formula over Γ has at least one model.  ...  M F C S 2 0 1 6 A Preliminary Investigation of Satisfiability Problems Not Harder Than 1-In-3-SAT  ... 

Using CSP look-back techniques to solve exceptionally hard SAT instances [chapter]

Roberto J. Bayardo, Robert Schrag
1996 Lecture Notes in Computer Science  
Without them, most instances are "exceptionally hard" -orders of magnitude harder than typical Random 3-SAT instances with the same surface characteristics.  ...  While CNF propositional satisfiability (SAT) is a sub-class of the more general constraint satisfaction problem (CSP), conventional wisdom has it that some well-known CSP look-back techniques --including  ...  Acknowledgments We wish to thank Jimi Crawford for the Tableau executable and assistance in replicating its behavior.  ... 
doi:10.1007/3-540-61551-2_65 fatcat:lzziqwsq5rdw7e2cj73eftivpq

Balance and Filtering in Structured Satisfiable Problems (Preliminary Report)

Henry Kautz, Yongshao Ruan, Dimitris Achlioptas, Carla Gomes Bart Selman, Mark Stickel
2001 Electronic Notes in Discrete Mathematics  
We investigate how this and other generators are biased away from the uniform distribution of satisfiable problems and show how they can be improved by imposing a balance condition.  ...  We also discuss the critical role of the problem encoding in the performance of both systematic and local search solvers.  ...  Next, we introduce a new satisfiable problem model, balanced QWH, which creates problems that are even harder than those found by filtered QCP, as summarized in the last line of Table 1 .  ... 
doi:10.1016/s1571-0653(04)00310-5 fatcat:p3ovbo6yhjaavgbm7t47hpozcy

Exponential complexity of the quantum adiabatic algorithm for certain satisfiability problems

Itay Hen, A. P. Young
2011 Physical Review E  
We determine the complexity of several constraint satisfaction problems using the quantum adiabatic algorithm in its simplest implementation.  ...  We also compare our results against the complexity of the analogous classical algorithm WalkSAT and show that the harder the problem is for the classical algorithm the harder it is also for the quantum  ...  This work is supported in part by the National Security Agency (NSA) under Army Research Office (ARO) contract number W911NF-09-1-0391, and in part by the National Science Foundation under Grant No.  ... 
doi:10.1103/physreve.84.061152 pmid:22304085 fatcat:zmlrz535yzg47nbkvdqiqyktou

Let the Solver Deal with Redundancy

Cédric Piette
2008 2008 20th IEEE International Conference on Tools with Artificial Intelligence  
However, this issue is not actually addressed in practice in modern SAT solvers, and is most of the time just ignored.  ...  For instance, the complexity of some redundancy-related problems for CNF formulae and for their 2-SAT and Horn SAT fragments have been recently studied.  ...  Σ, since (Σ\{φ 1 })|φ 1 is clearly un- satisfiable. The clauses φ 2 =¬a ∨ b ∨ c, φ 3 =a ∨ ¬b and φ 4 =¬a ∨ c ∨ ¬d are also redundant w.r.t. Σ.  ... 
doi:10.1109/ictai.2008.38 dblp:conf/ictai/Piette08 fatcat:bu5iguxurjcyzkxagfobujsmhm

Underestimation vs. Overestimation in SAT-Based Planning [chapter]

Mauro Vallati, Lukáš Chrpa, Andrew Crampton
2013 Lecture Notes in Computer Science  
Planning as satisfiability is one of the main approaches to finding parallel optimal solution plans for classical planning problems.  ...  technique for solving a given planning problem.  ...  The authors would like to acknowledge the use of the University of Huddersfield Queensgate Grid in carrying out this work.  ... 
doi:10.1007/978-3-319-03524-6_24 fatcat:zgiczbvwdjeg7cd7dkxsauadfi

Generating hard satisfiability problems

Bart Selman, David G. Mitchell, Hector J. Levesque
1996 Artificial Intelligence  
Our results provide a benchmark for the evaluation of satisfiability testing procedures.  ...  We report results from large-scale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy.  ...  Acknowledgements We thank James Crawford and Larry Auton for providing us with their very efficient tableau code, which we modified to obtain a fast implementation of DP.  ... 
doi:10.1016/0004-3702(95)00045-3 fatcat:w4lhubloabgglmeg7lw4c7rgza

Functional Test Generation Using Constraint Logic Programming [chapter]

Zhihong Zeng, Maciej Ciesielski, Bruno Rouzeyre
2002 IFIP Advances in Information and Communication Technology  
The generation of functional test vectors, guided by miscellaneous coverage metrics to satisfy the simulation target, can be posed as a satisfiability problem (SAT).  ...  This paper presents a novel approach to solving SAT based on Constraint Logic Programming technique.  ...  Assume that we are using a unified approach to solve a SAT problem in Figure 3 (a), where in the middle of a Branch-and-Bound process the objectives k=1 and 1=1 have to be justified.  ... 
doi:10.1007/978-0-387-35597-9_32 fatcat:uhmy4a7uxrgbnj2tq2eaiepclq

Backbone Guided Local Search for Maximum Satisfiability

Weixiong Zhang, Ananda Rangan, Moshe Looks
2003 International Joint Conference on Artificial Intelligence  
In this paper, we first investigate the effectiveness of Walksat, one of the best local search algorithms designed for SAT, on Max-SAT.  ...  Maximum satisfiability (Max-SAT) is more general and more difficult to solve than satisfiability (SAT).  ...  On harder satisfiable instances (Table 2 ), BGWalksat outperforms Walksat in all but two of 34 instances, where it is less than half a percent worse.  ... 
dblp:conf/ijcai/ZhangRL03 fatcat:5vonoc7isfekveedk3rbjh6mc4

Modelling More Realistic SAT Problems [chapter]

Andrew Slater
2002 Lecture Notes in Computer Science  
This work justifies and investigates a randomised satisfiability problem model with modular properties akin to those observed in real world search problem domains.  ...  Real world search problem benchmarks are not plentiful, yet understanding search algorithm behaviour in the real world domain is highly important.  ...  For higher values of percentage links the problems are more like the single cluster, or basic random 3-SAT, and are harder to solve than the problems with well defined clustering.  ... 
doi:10.1007/3-540-36187-1_52 fatcat:woiczfflufb6zohhvyxknmquxi

A SAT-based solver for Q-ALL SAT

B. Browning, A. Remshagen
2006 Proceedings of the 44th annual southeast regional conference on - ACM-SE 44  
We identify such a problem, called Q-ALL SAT, that arises in a variety of applications.  ...  Although the satisfiability problem (SAT) is NP-complete, state-of-the-art solvers for SAT can solve instances that are considered to be very hard.  ...  In particular, we have reduced the problem to a sequence of satisfiability problems (SAT) which demand to evaluate a propositional logic formula.  ... 
doi:10.1145/1185448.1185456 dblp:conf/ACMse/BrowningR06 fatcat:vd4y672sl5exflmje5bukuv52i

A Monte Carlo Tree Search Based Conflict-Driven Clause Learning SAT Solver

Jens Schloeter
2017 Jahrestagung der Gesellschaft für Informatik  
While a MCTS-based algorithm was successfully used to solve SAT problems, a number of established SAT solving techniques like clause learning and parallelization were not included in the algorithm.  ...  in using it to solve SAT problems.  ...  Fig. 1 : 1 Fig. 1: Encountering a conflicting node during the selection phase Fig. 2 : 2 Fig. 2: The search tree of Figure 1 after pruning nodes Fig. 3 : 3 Fig. 3: Average running time in milliseconds  ... 
doi:10.18420/in2017_257 dblp:conf/gi/Schloeter17 fatcat:m2pboqis2baglosuzqye6xmaha

Phase Transition in Unrestricted Random SAT [article]

Bernd R. Schuh
2012 arXiv   pre-print
The critical density m/n turns out to be strongly n-dependent, ccr = ln(2)/(1-p)^^n, where pn is the mean number of positive literals per clause.This is in contrast to restricted random SAT problems (random  ...  In contrast to random K-SAT, the method does not fail for the unrestricted model, because long range interactions between solutions are not cut off by disorder.  ...  On the other hand, they are interesting because the hardest problems of random SAT with mixed clause lengths can be magnitudes harder than those of fixed K models, [5] .  ... 
arXiv:1204.1656v1 fatcat:5akbcwsuizhhtnwyt6ryen3zkq

A Dynamic Clause Specific Initial Weight Assignment for Solving Satisfiability Problems Using Local Search

Abdelraouf Ishtaiwi, Feda Alshahwan, Naser Jamal, Wael Hadi, Muhammad AbuArqoub
2021 Algorithms  
, (3) clauses large in size and linked with a small neighborhood, and (4) clauses large in size and linked with a large neighborhood.  ...  Based on our examination, we categorized the clauses into four categories: (1) clauses small in size and linked with a small neighborhood, (2) clauses small in size and linked with a large neighborhood  ...  The funders had no role in the design of the study; in the collection, analyses, or interpretation of data.  ... 
doi:10.3390/a14010012 fatcat:7ymjof44mrctlfq7hisl3sy2z4

Analysis and extension of the Inc* on the satisfiability testing problem

Mohamed Bader-El-Den, Riccardo Poli
2008 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)  
Preliminary experiments on the satisfiability problem (SAT) problem have shown that Inc* is a competitive approach.  ...  Rather than attempting to directly solve a difficult problem, the algorithm dynamically chooses a smaller instance of the problem, and then increases the size of the instance only after the previous simplified  ...  it to the SAT problem, where, in preliminary experiments, Inc* appeared to be a competitive approach.  ... 
doi:10.1109/cec.2008.4631250 dblp:conf/cec/Bader-El-DenP08 fatcat:52vamwyabnc2ndiwmarutodb5m
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