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Optimal Implementation of Watched Literals and More General Techniques

I. P. Gent
2013 The Journal of Artificial Intelligence Research  
Techniques like watched literals are known to be highly space efficient and effective in practice.  ...  The result applies to a simple general framework, which I present: applications include watched literal unit propagation in SAT and a number of examples in constraint satisfaction.  ...  Acknowledgments I thank Chris Jefferson and Peter Nightingale for help with this paper in many ways, for example C++ coding advice and suggestions on how to implement variants of watched literals in MiniSat  ... 
doi:10.1613/jair.4016 fatcat:wnq2vlr3vne6bby4iycvflafmq

PicoSAT Essentials

Armin Biere, Ewald Speckenmeyer, Chu Min Li, Vasco Manquinho, Armando Tacchella
2008 Journal on Satisfiability, Boolean Modeling and Computation  
In this article we describe and evaluate optimized compact data structures for watching literals.  ...  We also discuss how to store proof traces compactly in memory and further unique features of PicoSAT including an aggressive restart schedule.  ...  They have their origin in new algorithms and heuristics but also in low-level optimization techniques.  ... 
doi:10.3233/sat190039 fatcat:2dxi5rynifgynioputxlyqhqg4

CafeSat

Régis Blanc
2013 Proceedings of the 4th Workshop on Scala - SCALA '13  
CafeSat is a modern solver based on DPLL and featuring many state-of-the-art techniques and heuristics.  ...  It uses two-watched literals for Boolean constraint propagation, conflict-driven learning along with clause deletion, a restarting strategy, and the VSIDS heuristics for choosing the branching literal.  ...  Acknowledgments The author would like to thank Viktor Kuncak and Alexandre Duc for comments on this report, as well as Philippe Suter for precious advices on implementation details.  ... 
doi:10.1145/2489837.2489839 dblp:conf/ecoop/Blanc13 fatcat:cirggj2y7jfuzdfqg7ycinbkdq

Efficient data structures for backtrack search SAT solvers

Inês Lynce, João Marques-Silva
2004 Annals of Mathematics and Artificial Intelligence  
Acknowledgements This work is partially supported by the European research project IST-2001-34607 and by Fundação para a Ciência e Tecnologia under research projects PRAXIS/C/EEI/ 11249/98 and POSI/34504  ...  Handling special cases: B/T clauses As one final optimization to literal sifting, we propose the special handling of the clauses that are more common in problem instances: binary and ternary clauses.  ...  Chaff's watched literals The more recent Chaff SAT solver [14] proposed a new data structure, the Watched Literals (WL), that solves some of the problems posed by H/T lists.  ... 
doi:10.1007/s10472-005-0425-5 fatcat:kg5hxhbt5ffqddmet7oq4jywmm

Efficient Data Structures for Backtrack Search SAT Solvers

In�s Lynce, Jo�o Marques-Silva
2005 Annals of Mathematics and Artificial Intelligence  
Acknowledgements This work is partially supported by the European research project IST-2001-34607 and by Fundação para a Ciência e Tecnologia under research projects PRAXIS/C/EEI/ 11249/98 and POSI/34504  ...  Handling special cases: B/T clauses As one final optimization to literal sifting, we propose the special handling of the clauses that are more common in problem instances: binary and ternary clauses.  ...  Chaff's watched literals The more recent Chaff SAT solver [14] proposed a new data structure, the Watched Literals (WL), that solves some of the problems posed by H/T lists.  ... 
doi:10.1007/s10472-004-9425-0 fatcat:ohik7dbw3be4pko32zvmzumg3e

SAT with partial clauses and back-leaps

S. Pilarski, G. Hu
2002 Proceedings 2002 Design Automation Conference (IEEE Cat. No.02CH37324)  
These optimization techniques can be combined with SAT mechanisms used in Chaff, SATO, and GRASP to develop a new solver that significantly outperforms its predecessors on a large set of benchmarks.  ...  This paper presents four new powerful SAT optimization techniques: partial clauses, back-leaps, immediate implications, and local decisions.  ...  In our implementation, validity of a partial clause is linked to the highest decision level associated with eliminated literals. Partial clause inherits watched literals from its parent clause.  ... 
doi:10.1109/dac.2002.1012721 fatcat:ci22hjghizbe7kikggd22ghyji

SAT with partial clauses and back-leaps

Slawomir Pilarski, Gracia Hu
2002 Proceedings - Design Automation Conference  
These optimization techniques can be combined with SAT mechanisms used in Chaff, SATO, and GRASP to develop a new solver that significantly outperforms its predecessors on a large set of benchmarks.  ...  This paper presents four new powerful SAT optimization techniques: partial clauses, back-leaps, immediate implications, and local decisions.  ...  In our implementation, validity of a partial clause is linked to the highest decision level associated with eliminated literals. Partial clause inherits watched literals from its parent clause.  ... 
doi:10.1145/513918.514104 dblp:conf/dac/PilarskiH02 fatcat:4sr3qe5g5nbsrdnl4yzpj26rzu

SAT with partial clauses and back-leaps

Slawomir Pilarski, Gracia Hu
2002 Proceedings - Design Automation Conference  
These optimization techniques can be combined with SAT mechanisms used in Chaff, SATO, and GRASP to develop a new solver that significantly outperforms its predecessors on a large set of benchmarks.  ...  This paper presents four new powerful SAT optimization techniques: partial clauses, back-leaps, immediate implications, and local decisions.  ...  In our implementation, validity of a partial clause is linked to the highest decision level associated with eliminated literals. Partial clause inherits watched literals from its parent clause.  ... 
doi:10.1145/514100.514104 fatcat:2on6raa2irafxlebxlgiatjio4

QuteSAT: A Robust Circuit-based SAT Solver for Complex Circuit Structure

Chi-An Wu, Ting-Hao Lin, Chih-Chun Lee, Chung-Yang Huang
2007 2007 Design, Automation & Test in Europe Conference & Exhibition  
Several novel techniques are proposed in this paper, including: (1) a generic watching scheme on general gate types for efficient Boolean Constraint Propagation (BCP), (2) an implicit implication graph  ...  We also demonstrate that by applying a simple circuitoriented decision ordering technique (J-frontier), our solver can constantly outperform the CNF ones for more than 15+ times.  ...  Note that circuit SAT also provides the flexibility in storing and optimizing the learned information into different formats. For example, multi-level logic or more general constraints, etc.  ... 
doi:10.1109/date.2007.364479 fatcat:aa7maojxwzellpxkhptngccpwm

Watched Literals for Constraint Propagation in Minion [chapter]

Ian P. Gent, Chris Jefferson, Ian Miguel
2006 Lecture Notes in Computer Science  
We describe three important aspects of watched literals as we apply them to constraints, and how they are implemented in the Minion constraint solver.  ...  We show that watched literals, already a great success in the satisfiability community, can be used to provide highly efficient implementations of constraint propagators.  ...  Our approach is only novel in being incorporated in a constraint solver: watched literals for the (more general) weighted sum of a Boolean array was reported by Chai and Kuehlmann [5] .  ... 
doi:10.1007/11889205_15 fatcat:wa5p54zhrfgczjy66za52rpgfy

The Sat4j library, release 2.2

Daniel Le Berre, Anne Parrain
2010 Journal on Satisfiability, Boolean Modeling and Computation  
Lazy data structure The library provides two implementations of a lazy data structure for SAT: the classical watched literals as found in Minisat, using literals move to front (from Picosat) and an implementation  ...  The former is easier and more elegant to implement. The latter has not been patented.  ... 
doi:10.3233/sat190075 fatcat:nnjdixv4abggli56b4aondmmei

Computing prime implicants

David Deharbe, Pascal Fontaine, Daniel Le Berre, Bertrand Mazure
2013 2013 Formal Methods in Computer-Aided Design  
generalized constraints (3) for clauses and, more generally for cardinality constraints, the algorithm complexity is linear in the size of the constraints found.  ...  The original aspects are (1) the algorithm is based on watched literals and a form of propagation of required literals, adapted to CDCL solvers (2) the algorithm works not only on clauses, but also on  ...  One such concrete implementation is given for clauses and, more generally, for cardinality constraints in Algorithm 6.  ... 
doi:10.1109/fmcad.2013.6679390 fatcat:mdenuxkczfeg5deiedgyyapjha

A verified SAT solver with watched literals using imperative HOL

Mathias Fleury, Jasmin Christian Blanchette, Peter Lammich
2018 Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018  
Based on our earlier formalization of conflict-driven clause learning (CDCL) in Isabelle/HOL, we refine the CDCL calculus to add a crucial optimization: two watched literals.  ...  Through a chain of refinements carried out using the Isabelle Refinement Framework, we target Imperative HOL and extract imperative Standard ML code.  ...  Acknowledgments Max Haslbeck, Anders Schlichtkrull, Mark Summerfield, and the anonymous reviewers suggested many textual improvements.  ... 
doi:10.1145/3176245.3167080 fatcat:nkb3who2ujhixesomqrvo2dc3i

Search techniques for SAT-based Boolean optimization

Fadi A. Aloul
2006 Journal of the Franklin Institute  
In this paper, we describe two methods to solve Boolean optimization problems using SAT solvers. Both methods are implemented and evaluated using the SAT solver PBS.  ...  One of the main advances in SAT is generalizing SAT solvers to handle stronger representation of constraints.  ...  Clearly, the PB encoding, consisting of six PB constraints and 18 literals, is more efficient than the CNF encoding, consisting of 12 clauses and 27 literals.  ... 
doi:10.1016/j.jfranklin.2006.01.003 fatcat:gay5fwpibrfvbc7tqzffkhranm

Chaff

Matthew W. Moskewicz, Conor F. Madigan, Ying Zhao, Lintao Zhang, Sharad Malik
2001 Proceedings of the 38th conference on Design automation - DAC '01  
efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy.  ...  Boolean Satisfiability is probably the most studied of combinatorial optimization/search problems.  ...  Figure 1 illustrates this technique. It shows how the watched literals for a single clause change under a series of assignments and unassignments.  ... 
doi:10.1145/378239.379017 dblp:conf/dac/MoskewiczMZZM01 fatcat:zbn4w54guvfxji2nssfhteetme
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