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Combining SAT Methods with Non-Clausal Decision Heuristics

Clark Barrett, Jacob Donham
2005 Electronical Notes in Theoretical Computer Science  
We show how to combine some Boolean SAT methods with non-clausal heuristics developed for first-order decision procedures.  ...  A decision procedure for arbitrary first-order formulas can be viewed as combining a propositional search with a decision procedure for conjunctions of first-order literals, so Boolean SAT methods can  ...  We can combine SAT methods with non-clausal heuristics developed for first-order decision procedures to obtain a method which takes fewer decisions to decide a formula than either one by itself.  ... 
doi:10.1016/j.entcs.2004.09.042 fatcat:irugjv7wq5fivie6bxjpbztwci

An Experimental Evaluation of Ground Decision Procedures [chapter]

Leonardo de Moura, Harald Rueß
2004 Lecture Notes in Computer Science  
We develop maps of the behavior of ground decision procedures by comparing the performance of a variety of technologies on benchmark suites with differing characteristics.  ...  There is a large variety of algorithms for ground decision procedures, but their differences, in particular in terms of experimental performance, are not well studied.  ...  It realizes a lazy, online integration of a non-clausal SAT solver with an incremental, backtrackable constraint engine based on a Shostak [11] combination.  ... 
doi:10.1007/978-3-540-27813-9_13 fatcat:vtodfjv6mrcknhl4vghsmdxvti

Solving Non-clausal Formulas with DPLL Search [chapter]

Christian Thiffault, Fahiem Bacchus, Toby Walsh
2004 Lecture Notes in Computer Science  
Great progress has been made on DPLL based SAT solvers operating on CNF encoded SAT theories. However, for most problems CNF is not a very natural representation.  ...  In particular, we demonstrate that a SAT solver which operates directly on a propositional formula, can achieve the same efficiency as a highly optimized modern CNF SAT solver.  ...  Then we present a method for performing DPLL search with a non-clausal encoding, and discuss the implementation techniques we utilized to obtain efficient inference on the non-clausal encoding.  ... 
doi:10.1007/978-3-540-30201-8_48 fatcat:dsuz5dylfnbofbi2zrw3xpqxpq

Sets with Cardinality Constraints in Satisfiability Modulo Theories [chapter]

Philippe Suter, Robin Steiger, Viktor Kuncak
2011 Lecture Notes in Computer Science  
NC(T ) remove this constraint by extending the Boolean engine to support the detection of implications and conflicts on non-clausal constraints, using techniques working on graphical representations of  ...  This thesis presents NC(T ), an extension of the DPLL(T ) scheme [16, 29] for decision procedures for quantifier-free first-order logics.  ...  [34] presents another attempt at a non-clausal SAT solver.  ... 
doi:10.1007/978-3-642-18275-4_28 fatcat:kohimod67vc6fefogtu6klxka4

The design and implementation of the model constructing satisfiability calculus

Dejan Jovanovic, Clark Barrett, Leonardo de Moura
2013 2013 Formal Methods in Computer-Aided Design  
combined.  ...  We report encouraging experimental results, where MCSat performs competitive with the state-of-the art SMT solvers without using pre-processing techniques and ad-hoc optimizations.  ...  The heuristic is based on how often a variable is used in conflict resolution, and is popularly used in CDCL-style SAT solvers [3] .  ... 
doi:10.1109/fmcad.2013.7027033 fatcat:d2aetdpvpngprmfqlo4ujkfxzq

A Clausal Genetic Representation and its Evolutionary Procedures for Satisfiability Problems [chapter]

Jin-Kao Hao
1995 Artificial Neural Nets and Genetic Algorithms  
This paper presents a clausal genetic representation for the satisfiability problem (SAT).  ...  Various fitness functions for measuring clausal individuals are identified and their relative merits analyzed. Some preliminary resluts are reported.  ...  Note that 3-SAT is the preferred form of many studies, and most methods mentioned above deal with 3-SAT instances. Given a 3-SAT instance F ≡ C1∧C2∧...∧CL containing N different variables.  ... 
doi:10.1007/978-3-7091-7535-4_76 dblp:conf/icannga/Hao95 fatcat:trnglwqgpbhezeylisd3tdroeu

A Hybrid BDD and SAT Finite Domain Constraint Solver [chapter]

Peter Hawkins, Peter J. Stuckey
2005 Lecture Notes in Computer Science  
Boolean Satisfiability (SAT) solvers are another form of constraint solver that operate on constraints on Boolean variables expressed in clausal form.  ...  Modern SAT solvers have highly optimized propagation mechanisms and also incorporate efficient conflict-clause learning algorithms and effective search heuristics based on variable activity, but these  ...  Dechter [7] , chapter 6), but there seems little evidence of success for look back methods that combine with propagation.  ... 
doi:10.1007/11603023_8 fatcat:hyihg3ci4zf35mehqc667ugfsq

SAT and Interactions (Dagstuhl Seminar 20061)

Olaf Beyersdorff, Uwe Egly, Meena Mahajan, Cláudia Nalon
2020 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 20061 "SAT and Interactions".  ...  fields and embarked on an interdisciplinary exchange of ideas and techniques between these neighbouring subfields of SAT.  ...  We present the spinal atomic lambda-calculus, a typed lambda-calculus with explicit sharing and atomic duplication that achieves spinal full laziness: duplicating only the direct paths between a binder  ... 
doi:10.4230/dagrep.10.2.1 dblp:journals/dagstuhl-reports/BeyersdorffEMN20 fatcat:q6vjxmce4bd2nkm3vym2qkvqam

Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer [chapter]

Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek
2016 Lecture Notes in Computer Science  
An important role is played by dedicated look-ahead heuristics, which indeed allowed to solve the problem on a cluster with 800 cores in about 2 days.  ...  We solve this problem, proving in fact the impossibility, by using the Cube-and-Conquer paradigm, a hybrid SAT method for hard problems, employing both look-ahead and CDCL solvers.  ...  The intuition behind this combination of paradigms is that look-ahead heuristics focus on global decisions, while CDCL heuristics focus on local decisions.  ... 
doi:10.1007/978-3-319-40970-2_15 fatcat:kiqj5ts7ivfkflzgpskdflpyhm

Satisfiability Checking of Non-clausal Formulas Using General Matings [chapter]

Himanshu Jain, Constantinos Bartzis, Edmund Clarke
2006 Lecture Notes in Computer Science  
We present a new non-clausal SAT-solver based on General Matings instead of DPLL search.  ...  Experimental results show that our SAT solver is competitive to current state-of-the-art SAT solvers on a class of non-clausal benchmarks.  ...  Acknowledgment: We thank Peter Andrews for his useful comments and Malay Ganai, Guoqiang Pan, Sanjit Seshia, Volker Sorge for providing us with benchmarks.  ... 
doi:10.1007/11814948_10 fatcat:tjdfal3tkrc4jeuvy23gwxxpje

An AIG-Based QBF-solver using SAT for preprocessing

Florian Pigorsch, Christoph Scholl
2010 Proceedings of the 47th Design Automation Conference on - DAC '10  
We use a new quantifier elimination method for AIGs, which heuristically combines cofactor-based quantifier elimination with quantification using BDDs and thus benefits from the strengths of both data  ...  Moreover, we present a novel SAT-based method for preprocessing QBFs that is able to efficiently detect variables with forced truth assignments, allowing for an elimination of these variables from the  ...  decision heuristics ("Constant Detection (original decision heuristics)"), and one which includes constant detection along with the proposed modification of the decision heuristics ("Constant Detection  ... 
doi:10.1145/1837274.1837318 dblp:conf/dac/PigorschS10 fatcat:nfvxrtnuujhgdfhtev7hugx6hy

CDCL-inspired Word-level Learning for Bit-vector Constraint Solving [article]

Zakaria Chihani, François Bobot, Sébastien Bardin
2017 arXiv   pre-print
We propose a conflict-driven, word-level, combinable constraints learning for the theory of quantifier-free bit-vectors.  ...  This work paves the way to truly word-level decision procedures for bit-vectors, taking full advantage of word-level propagations recently designed in CP and SMT communities.  ...  The approach uses a non-clausal learning that relies on direct inference between the constraints themselves as well as SAT inspired techniques, notably a similar heuristic to VSIDS [3] for variable ordering  ... 
arXiv:1706.09229v1 fatcat:ycupitqgzfh4pmxfgixmwp2sci

Clause Learning and New Bounds for Graph Coloring

Emmanuel Hebrard, George Katsirelos
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
We introduce a new lower bound for this problem based on Mycielskian graphs; a method to produce a clausal explanation of this bound for use in a CDCL algorithm; and a branching heuristic emulating Brelaz  ...  We introduce a hybrid CP/SAT approach to graph coloring based on exploring Zykov's tree: for two non-neighbors, either they take a different color and there might as well be an edge between them, or they  ...  For every non-edge (uv), the edge variable e uv stands for the decision of contracting the vertices (e uv = 1), or adding the edge (e uv = 0).  ... 
doi:10.24963/ijcai.2019/856 dblp:conf/ijcai/HebrardK19 fatcat:ypjb6xlx2racxapzds63xgonla

Computing Optimal Decision Sets with SAT [article]

Jinqiang Yu, Alexey Ignatiev, Peter J. Stuckey, Pierre Le Bodic
2020 arXiv   pre-print
By finding optimal solutions we show we can build decision set classifiers that are almost as accurate as the best heuristic methods, but far more concise, and hence more explainable.  ...  This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule.  ...  sets quickly with accuracy comparable to the best heuristic methods, but much smaller.  ... 
arXiv:2007.15140v1 fatcat:kotj77rbazcv3anbnfpb2lvxju

Dsharp: Fast d-DNNF Compilation with sharpSAT [chapter]

Christian Muise, Sheila A. McIlraith, J. Christopher Beck, Eric I. Hsu
2012 Lecture Notes in Computer Science  
Knowledge compilation is a compelling technique for dealing with the intractability of propositional reasoning.  ...  We exploit recent advances in #SAT solving in order to produce a new state-ofthe-art CNF → d-DNNF compiler: DSHARP.  ...  In IBCP, a subset of the unassigned variables are heuristically chosen at a decision node and the impact of assigning any one of them is evaluated.  ... 
doi:10.1007/978-3-642-30353-1_36 fatcat:lzu5cavdbzbgnhtwy2ggl2glge
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