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Practical algorithms for unsatisfiability proof and core generation in SAT solvers

Roberto Asín Achá, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell
2010 AI Communications  
The second part of this article is about in-memory algorithms for generating SAT proofs and cores, without writing traces to disk.  ...  resolution proof can be extracted (and checked), and hence also an unsatisfiable core: a (frequently small) unsatisfiable subset of the input clauses.  ...  Practical Algorithms for Unsatisfiability Proof and Core Generation in SAT solvers Roberto [ZM03] , it is well-known that modern DPLL-based SAT solvers with learning can be instrumented to write a  ... 
doi:10.3233/aic-2010-0462 fatcat:fihrqip7ojeaxkf4znljt5h4va

On Using Unsatisfiability for Solving Maximum Satisfiability [article]

Joao Marques-Silva, Jordi Planes
2007 arXiv   pre-print
Moreover, the efficiency of the new generation of unsatisfiability-based MaxSAT solvers becomes effectively indexed to the ability of modern SAT solvers to proving unsatisfiability and identifying unsatisfiable  ...  Recent work proposed using efficient Boolean Satisfiability (SAT) solvers for solving the MaxSAT problem, based on identifying and eliminating unsatisfiable subformulas.  ...  This work is partially supported by EU project IST/033709 and by EPSRC grant EP/E012973/1.  ... 
arXiv:0712.1097v1 fatcat:on7wlndgdfc7hau5hhkv4udgpi

On Computing Minimum Unsatisfiable Cores

Inês Lynce, João P. Marques Silva
2004 International Conference on Theory and Applications of Satisfiability Testing  
Nevertheless, in the utilization of SAT in industrial settings, one often needs to be able to generate unsatisfiability proofs, either to guarantee the correctness of the SAT solver or as part of the utilization  ...  Certifying a SAT solver for unsatisfiable instances is a computationally hard problem.  ...  the ability of SAT solvers for generating proofs of unsatisfiability and for computing unsatisfiable cores.  ... 
dblp:conf/sat/LynceM04 fatcat:w56e56w6jrc7dinz2un6rlaude

Efficient Generation of Unsatisfiability Proofs and Cores in SAT [chapter]

Roberto Asín, Robert Nieuwenhuis, Albert Oliveras, Enric Rodríguez-Carbonell
2008 Lecture Notes in Computer Science  
Some modern DPLL-based propositional SAT solvers now have fast in-memory algorithms for generating unsatisfiability proofs and cores without writing traces to disk.  ...  However, in long SAT runs these algorithms still run out of memory.  ...  The differences in runtime between our basic SAT solver without proof/core generation and its versions that do the necessary bookkeeping for in-memory proof/core generation are always very small, usually  ... 
doi:10.1007/978-3-540-89439-1_2 fatcat:oraa3edgsrfstcrpchuwee3sam

Validating the result of a Quantified Boolean Formula (QBF) solver

Yinlei Yu, Sharad Malik
2005 Proceedings of the 2005 conference on Asia South Pacific design automation - ASP-DAC '05  
It also presents a mechanism to extract small unsatisfiable subformulas, called cores, from unsatisfiable QBF instances.  ...  This paper demonstrates a methodology for independently validating the results of a DLL based QBF solver using the traces generated during the solving process.  ...  Also, we propose methods to extract unsatisfiable core for false QBF instances that have been shown to be efficient and result in small cores in practice.  ... 
doi:10.1145/1120725.1120821 dblp:conf/aspdac/YuM05 fatcat:s5fi3dqgmfgyzmhm6w6vggtram

On Validating Boolean Optimizers [article]

Antonio Morgado, Joao Marques-Silva
2011 arXiv   pre-print
This entails implementing solutions for validating both satisfiable and unsatisfiable answers from the NP oracle.  ...  The increasing use of Boolean optimizers in practical settings raises the question of confidence in computed results. For example, the issue of confidence is paramount in safety critical settings.  ...  The paper overviews all existing algorithms based on iterative calls to a SAT solver, and shows that, for all these algorithms, it suffices to check one unsatisfiability proof and one satisfiable certificate  ... 
arXiv:1109.2752v1 fatcat:yzjboh7g45attpigydap3h3wvi

On Improving MUS Extraction Algorithms [chapter]

Joao Marques-Silva, Ines Lynce
2011 Lecture Notes in Computer Science  
The first algorithm is optimal in its class, meaning that it requires the smallest number of calls to a SAT solver.  ...  Minimally Unsatisfiable Subformulas (MUS) find a wide range of practical applications, including product configuration, knowledge-based validation, and hardware and software design and verification.  ...  Our approach considers solely the computed unsatisfiable core, and so allows using the SAT solver as a black box (provided the solver returns an unsatisfiable core).  ... 
doi:10.1007/978-3-642-21581-0_14 fatcat:3tdlrcv3pngkvnvs4qfvqflqxe

Abstraction Refinement for Bounded Model Checking [chapter]

Anubhav Gupta, Ofer Strichman
2005 Lecture Notes in Computer Science  
Our technique makes bmc much faster, as indicated by our experiments. bmc is also used for generating refinements in the Proof-Based Refinement (pbr) framework.  ...  We show that our technique unifies pbr and cegar into an abstraction-refinement framework that can balance the model checking and refinement efforts.  ...  The first author would like to thank Ken McMillan for useful discussions.  ... 
doi:10.1007/11513988_11 fatcat:khc5uoohundthiswijrtwfkwgi

Algorithms for Maximum Satisfiability Using Unsatisfiable Cores [chapter]

Joao Marques-Sila, Jordi Planes
2010 Advanced Techniques in Logic Synthesis, Optimizations and Applications  
The new algorithm exploits modern SAT solvers, being based on the identification of unsatisfiable subformulas.  ...  Algorithms for MaxSAT are still fairly inefficient in industrial settings, in part because the most effective SAT techniques cannot be easily extended to MaxSAT.  ...  Instead of the usual algorithms for MaxSAT, the proposed algorithm exploits existing SAT solver technology, and the ability of SAT solvers for finding unsatisfiable subformulas.  ... 
doi:10.1007/978-1-4419-7518-8_10 fatcat:mzavrgirvrdhzey4itokbsnzy4

Algorithms for Maximum Satisfiability using Unsatisfiable Cores

Joao Marques-Silva, Jordi Planes
2008 2008 Design, Automation and Test in Europe  
The new algorithm exploits modern SAT solvers, being based on the identification of unsatisfiable subformulas.  ...  Algorithms for MaxSAT are still fairly inefficient in industrial settings, in part because the most effective SAT techniques cannot be easily extended to MaxSAT.  ...  Instead of the usual algorithms for MaxSAT, the proposed algorithm exploits existing SAT solver technology, and the ability of SAT solvers for finding unsatisfiable subformulas.  ... 
doi:10.1109/date.2008.4484715 dblp:conf/date/Marques-SilvaP08 fatcat:y3xijl4ydje43fqqpvajhmtmny

Trimming while checking clausal proofs

Marijn J. H. Heule, Warren A. Hunt, Nathan Wetzler
2013 2013 Formal Methods in Computer-Aided Design  
Additionally, the quality of the additional results, such as unsatisfiable cores, is higher when compared to modified SAT solvers.  ...  Conflict-driven clause learning (CDCL) satisfiability solvers can emit more than a satisfiability result; they can also emit clausal proofs, resolution proofs, unsatisfiable cores, and Craig interpolants  ...  This suggests that resolution proofs are not a viable method for checking the unsatisfiability results in a general setting, such as the SAT Competition.  ... 
doi:10.1109/fmcad.2013.6679408 fatcat:a2qrloxspja6rf7wcbix7de24i

Generalizing Core-Guided Max-SAT [chapter]

Mark H. Liffiton, Karem A. Sakallah
2009 Lecture Notes in Computer Science  
With the technique's success in Max-SAT for industrial instances, our development of a generalized approach is motivated by the industrial applications of MCSes in circuit debugging [12] and as a precursor  ...  Recent work has shown the value of using unsatisfiable cores to guide maximum satisfiability algorithms (Max-SAT) running on industrial instances [5, 9, 10, 11] .  ...  Acknowledgments We thank João Marques-Silva for providing binaries for his MSU* algorithms. This material is based upon work supported by the National Science Foundation under ITR Grant No. 0205288.  ... 
doi:10.1007/978-3-642-02777-2_44 fatcat:i4m2yjw2tvhungvk5uvp2jb44q

Algorithms for maximum satisfiability using unsatisfiable cores

Joao Marques-Silva, Jordi Planes
2008 Proceedings of the conference on Design, automation and test in Europe - DATE '08  
The new algorithm exploits modern SAT solvers, being based on the identification of unsatisfiable subformulas.  ...  Algorithms for MaxSAT are still fairly inefficient in industrial settings, in part because the most effective SAT techniques cannot be easily extended to MaxSAT.  ...  Instead of the usual algorithms for MaxSAT, the proposed algorithm exploits existing SAT solver technology, and the ability of SAT solvers for finding unsatisfiable subformulas.  ... 
doi:10.1145/1403375.1403474 fatcat:brvpxwe2ovceda6e4nwbuzl4vm

Computing Small Unsatisfiable Cores in Satisfiability Modulo Theories

A. Cimatti, A. Griggio, R. Sebastiani
2011 The Journal of Artificial Intelligence Research  
The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification.  ...  This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas are removed. The approach is conceptually interesting, and has several advantages in practice.  ...  Acknowledgments We wish to thank Mark Liffiton for his help with the CAMUS tool. We also thank the anonymous referees for their helpful suggestions.  ... 
doi:10.1613/jair.3196 fatcat:epem5lkixzay3iumq52aamzun4

Deriving Small Unsatisfiable Cores with Dominators [chapter]

Roman Gershman, Maya Koifman, Ofer Strichman
2006 Lecture Notes in Computer Science  
core only for proving d) and attempts to prove them without the M clauses.  ...  The problem of finding a small unsatisfiable core of an unsatisfiable CNF formula is addressed.  ...  They suggested a simple and effective iterative procedure for deriving a small unsatisfiable core: they extract an unsatisfiable core from an unsatisfiability proof of the formula provided by a SAT solver  ... 
doi:10.1007/11817963_13 fatcat:q2a2zmd4dbc4to5fnhysj7aa7q
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