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Short proofs for tricky formulas
Acta Informatica
Artificial Intelligence
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BDD variable ordering for interacting finite state machines
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AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
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STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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SIAM Journal on Computing
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On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Dependent and Independent Variables in Propositional Satisfiability
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CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
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LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
On the Relation between SAT and BDDs for Equivalence Checking
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Computational Complexity
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SymChaff: a structure-aware satisfiability solver
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Measuring the hardness of SAT instances
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
On the power of top-down branching heuristics
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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ACM Transactions on Computation Theory (TOCT)
On Modern Clause-Learning Satisfiability Solvers
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SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Limitations of restricted branching in clause learning
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Generic tableaux for answer set programming
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Extended ASP tableaux and rule redundancy in normal logic programs
ICLP'07 Proceedings of the 23rd international conference on Logic programming
Compressing propositional proofs by common subproof extraction
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
On the power of clause-learning SAT solvers with restarts
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
A generalized framework for conflict analysis
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
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ICTAC'10 Proceedings of the 7th International colloquium conference on Theoretical aspects of computing
Exact cover via satisfiability: an empirical study
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Local consistency and SAT-solvers
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Heuristics for planning with SAT
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Extending clause learning of SAT solvers with Boolean Gröbner bases
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On the power of clause-learning SAT solvers as resolution engines
Artificial Intelligence
Propelling SAT and SAT-based BMC using careset
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Clause-learning algorithms with many restarts and bounded-width resolution
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Parameterized complexity of DPLL search procedures
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Faster extraction of high-level minimal unsatisfiable cores
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
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Generalized conflict-clause strengthening for satisfiability solvers
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Empirical study of the anatomy of modern sat solvers
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
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CSR'06 Proceedings of the First international computer science conference on Theory and Applications
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A note on SAT algorithms and proof complexity
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Planning with SAT, admissible heuristics and A*
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IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
An improved separation of regular resolution from pool resolution and clause learning
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Revisiting clause exchange in parallel SAT solving
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
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Local consistency and SAT-solvers
Journal of Artificial Intelligence Research
Planning as satisfiability: Heuristics
Artificial Intelligence
Relating proof complexity measures and practical hardness of SAT
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Producing and verifying extremely large propositional refutations
Annals of Mathematics and Artificial Intelligence
Tableau Calculi for Logic Programs under Answer Set Semantics
ACM Transactions on Computational Logic (TOCL)
Parameterized Complexity of DPLL Search Procedures
ACM Transactions on Computational Logic (TOCL)
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Soundness of inprocessing in clause sharing SAT solvers
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Concurrent clause strengthening
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
Mechanical verification of SAT refutations with extended resolution
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Implicit learning of common sense for reasoning
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Effcient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas.