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A Translation of Pseudo-Boolean Constraints to SAT

Olivier Bailleux, Yacine Boufkhad, Olivier Roussel, Daniel Le Berre, Laurent Simon
2006 Journal on Satisfiability, Boolean Modeling and Computation  
This paper introduces a new CNF encoding of pseudo-Boolean constraints, which allows unit propagation to maintain generalized arc consistency.  ...  The results provide new perspectives in the field of full CNF approach of pseudo-Boolean constraints solving.  ...  Acknowledgments The authors are grateful to the anonymous reviewers for their comments. We would like to thank Dominique Rossin for helpful discussions.  ... 
doi:10.3233/sat190021 fatcat:ibbnq76uxfhf3aelqqyt3yuq6q

Algorithms for Weighted Boolean Optimization [article]

Vasco Manquinho and Joao Marques-Silva and Jordi Planes
2009 arXiv   pre-print
Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form.  ...  The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT).  ...  There are also algorithms that encode pseudo-Boolean constraints into propositional clauses [33, 5, 15] and solve the problem by subsequently using a SAT solver.  ... 
arXiv:0903.0843v2 fatcat:gw46xr45nfhrholhb3wl5sfs6q

Algorithms for Weighted Boolean Optimization [chapter]

Vasco Manquinho, Joao Marques-Silva, Jordi Planes
2009 Lecture Notes in Computer Science  
Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form.  ...  The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT).  ...  There are also algorithms that encode pseudo-Boolean constraints into propositional clauses [33, 5, 15] and solve the problem by subsequently using a SAT solver.  ... 
doi:10.1007/978-3-642-02777-2_45 fatcat:w6t7iducw5ecxdj35oa7ho67xu

Improving Unsatisfiability-Based Algorithms for Boolean Optimization [chapter]

Vasco Manquinho, Ruben Martins, Inês Lynce
2010 Lecture Notes in Computer Science  
This paper proposes the use of Pseudo-Boolean Optimization (PBO) solvers as a preprocessor for unsatisfiability-based algorithms in order to increase its robustness.  ...  Moreover, the use of constraint branching, a well-known technique from Integer Linear Programming, is also proposed into the unsatisfiability-based framework.  ...  Finally, notice that the Equals1 constraint in line 20 does not need to be encoded into CNF, since a pseudo-Boolean solver is used instead of a SAT solver.  ... 
doi:10.1007/978-3-642-14186-7_16 fatcat:nfq3r2kzqvhi7gkce5bosqk2pa

BoolVar/PB v1.0, a java library for translating pseudo-Boolean constraints into CNF formulae [article]

Olivier Bailleux
2011 arXiv   pre-print
BoolVar/PB is an open source java library dedicated to the translation of pseudo-Boolean constraints into CNF formulae. Input constraints can be categorized with tags.  ...  Several encoding schemes are implemented in a way that each input constraint can be translated using one or several encoders, according to the related tags.  ...  Available encodings The current version of BoolVar/pb includes 5 cnf encoders for pseudo-Boolean inequality constraints.  ... 
arXiv:1103.3954v1 fatcat:zmvdjbnvkfhynf7tn2hhugfcaa

New Encodings of Pseudo-Boolean Constraints into CNF [chapter]

Olivier Bailleux, Yacine Boufkhad, Olivier Roussel
2009 Lecture Notes in Computer Science  
This paper answers affirmatively the open question of the existence of a polynomial size CNF encoding of pseudo-Boolean (PB) constraints such that generalized arc consistency (GAC) is maintained through  ...  From a theoretical point of view, this narrows the gap between the expressive power of clauses and the one of pseudo-Boolean constraints.  ...  Section 5 compares the new method with the previous encodings of PB constraints into SAT. At last, some perspectives are given.  ... 
doi:10.1007/978-3-642-02777-2_19 fatcat:b53ehfgq2nentesyom2jq4ts5e

Using interval constraint propagation for pseudo-Boolean constraint solving

Karsten Scheibler, Bernd Becker
2014 2014 Formal Methods in Computer-Aided Design (FMCAD)  
have difficulties in solving instances with huge pseudo-Boolean constraints as created by our application.  ...  This work is motivated by (1) a practical application which automatically generates test patterns for integrated circuits and (2) the observation that off-the-shelf state-of-the-art pseudo-Boolean solvers  ...  ACKNOWLEDGEMENTS The authors thank Leonore Winterer and Felix Neubauer as well as Dominik Erb and Linus Feiten for supporting this work.  ... 
doi:10.1109/fmcad.2014.6987614 dblp:conf/fmcad/ScheiblerB14 fatcat:5clihi34rfgxxnjsqa4zdoqtcy

On the CNF encoding of cardinality constraints and beyond [article]

Olivier Bailleux
2010 arXiv   pre-print
In this report, we propose a quick survey of the currently known techniques for encoding a Boolean cardinality constraint into a CNF formula, and we discuss about the relevance of these encodings.  ...  We also propose models to facilitate analysis and design of CNF encodings for Boolean constraints.  ...  On the other hand, Translating a clause into a pseudo-Boolean or cardinality constraint is immediate.  ... 
arXiv:1012.3853v1 fatcat:3pwyacgdaba4nkbosyks3sakf4

Portfolio solver for verifying Binarized Neural Networks

Gergely Kovásznai, Krisztián Gajdár, Nina Narodytska
2021 Annales Mathematicae et Informaticae  
In the paper we propose all the corresponding encodings of different types of BNN layers as well as BNN properties into SAT, SMT, cardinality constrains, and pseudo-Boolean constraints.  ...  We introduce our portfolio solver that is able to encode BNN properties for SAT, SMT, and MIP solvers and run them in parallel, in a portfolio setting.  ...  Encoding into pseudo-Boolean constraints The Boolean cardinality encoding from Section 4.3 can be fed into pseudo-Boolean solvers as well.  ... 
doi:10.33039/ami.2021.03.007 fatcat:pvigltjexzgftkdscfi6zojrjm

Counting Models in Integer Domains [chapter]

António Morgado, Paulo Matos, Vasco Manquinho, João Marques-Silva
2006 Lecture Notes in Computer Science  
The first approach consists of encoding ILP instances into pseudo-Boolean (PB) instances.  ...  A two-step procedure is proposed, consisting of first mapping the ILP instance into PB constraints and then encoding the PB constraints into SAT.  ...  The first approach consists of encoding instances of ILP into instances of pseudo-Boolean (PB) constraints.  ... 
doi:10.1007/11814948_37 fatcat:crplkqusw5ahjpmvcojoj6nis4

Generalized Totalizer Encoding for Pseudo-Boolean Constraints [article]

Saurabh Joshi, Ruben Martins, Vasco Manquinho
2015 arXiv   pre-print
A common approach to solve these constraints is to encode them into a SAT formula.  ...  The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded.  ...  Hence, the GAC proof still holds for GTE. Related Work The idea of encoding a PBC into a SAT formula is not new.  ... 
arXiv:1507.05920v1 fatcat:vmgo6nqhvzaabiujin4jtpikwy

Constraint Reductions [article]

Olivier Bailleux
2020 arXiv   pre-print
This is a commentary on the CP 2003 paper "Efficient cnf encoding of boolean cardinality constraints".  ...  After recalling its context, we outline a classification of Constraints with respect to their deductive power regarding General Arc Consistency (GAC).  ...  solver dedicated to a MPC Constraint, such as SAT solvers or even pseudo-Boolean solvers.  ... 
arXiv:2006.02081v1 fatcat:6ttphel2cfhdljnmhrywlr7umm

On Using Incremental Encodings in Unsatisfiability-based MaxSAT Solving

Ruben Martins, Saurabh Joshi, Vasco Manquinho, Inês Lynce
2015 Journal on Satisfiability, Boolean Modeling and Computation  
Finally, the proposed incremental encodings of cardinality and pseudo-Boolean constraints are not exclusive for MaxSAT usage and can be used in other domains. 1.  ...  Furthermore, we also propose to extend incrementality to weighted MaxSAT through an incremental encoding of pseudo-Boolean constraints.  ...  The pseudo-Boolean constraint is encoded into CNF and given to the SAT solver (line 7). Observe that a pseudo-Boolean constraint is only necessary for weighted MaxSAT.  ... 
doi:10.3233/sat190102 fatcat:4dzjdjr2bvckhpn3a2wrvstmmm

Certifying Parity Reasoning Efficiently Using Pseudo-Boolean Proofs

Stephan Gocht, Jakob Nordström
2021 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
For Boolean satisfiability (SAT) solvers proof logging has been introduced as a way to certify correctness, but the methods used seem hard to generalize to stronger paradigms.  ...  In this work, we show how to instead use pseudo-Boolean inequalities with extension variables to concisely justify XOR reasoning.  ...  Acknowledgments We want to thank Mate Soos and Kuldeep Meel for helpful discussions on how to implement Gaussian elimination modulo 2.  ... 
doi:10.1609/aaai.v35i5.16494 fatcat:zrdshh3efbeq3pp42kqr4imuzm

The Picat-SAT Compiler [chapter]

Neng-Fa Zhou, Håkan Kjellerstrand
2016 Lecture Notes in Computer Science  
SAT has become the backbone of many software systems. In order to make full use of the power of SAT solvers, a SAT compiler must encode domain variables and constraints into an efficient SAT formula.  ...  This paper gives the encoding algorithms for constraints, and attempts to experimentally justify the choices of the algorithms for the addition and multiplication constraints.  ...  As mentioned above, Picat-SAT splits pseudo-Boolean constraints into adders and comparators, as it does for other arithmetic constraints.  ... 
doi:10.1007/978-3-319-28228-2_4 fatcat:nzcmuorgvnb7hor2eoyhyyk6mq
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