Solving Hybrid Boolean Constraints by Fourier Expansions and Continuous Optimization

Solving Hybrid Boolean Constraints by Fourier Expansions and Continuous Optimization

[1]  Mark H. Liffiton,et al.  A Cardinality Solver: More Expressive Constraints for Free - (Poster Presentation) , 2012, SAT.

[2]  Weiwei Gong,et al.  A survey of SAT solver , 2017 .

[3]  J. R. Barbosa Applied Hilbert's Nullstellensatz for Combinatorial Problems , 2016 .

[4]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[5]  Henry Kautz,et al.  Exploiting Variable Dependency in Local Search , 1997, IJCAI 1997.

[6]  Surya Ganguli,et al.  Identifying and attacking the saddle point problem in high-dimensional non-convex optimization , 2014, NIPS.

[7]  T. Sanders,et al.  Analysis of Boolean Functions , 2012, ArXiv.

[8]  Kenneth E. Batcher,et al.  Sorting networks and their applications , 1968, AFIPS Spring Joint Computing Conference.

[9]  Joao Marques-Silva,et al.  PySAT: A Python Toolkit for Prototyping with SAT Oracles , 2018, SAT.

[10]  M. Thornton,et al.  Efficient Spectral Coefficient Calculation Using Circuit Output Probabilities , 1994 .

[11]  Irit Dinur,et al.  The Hardness of 3-Uniform Hypergraph Coloring , 2005, Comb..

[12]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.

[13]  Michael I. Jordan,et al.  Gradient Descent Converges to Minimizers , 2016, ArXiv.

[14]  Furong Huang,et al.  Escaping From Saddle Points - Online Stochastic Gradient for Tensor Decomposition , 2015, COLT.

[15]  Walter Kern,et al.  An improved deterministic local search algorithm for 3-SAT , 2004, Theor. Comput. Sci..

[16]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[17]  Toby Walsh,et al.  Decomposing Global Grammar Constraints , 2007, CP.

[18]  Vasco M. Manquinho,et al.  Exploiting Cardinality Encodings in Parallel Maximum Satisfiability , 2011, 2011 IEEE 23rd International Conference on Tools with Artificial Intelligence.

[19]  Gilles Audemard,et al.  Lazy Clause Exchange Policy for Parallel SAT Solvers , 2014, SAT.

[20]  Erika Ábrahám,et al.  Building Bridges between Symbolic Computation and Satisfiability Checking , 2015, ISSAC.

[21]  A. Bonami Étude des coefficients de Fourier des fonctions de $L^p(G)$ , 1970 .

[22]  Moshe Y. Vardi,et al.  Combining the k-CNF and XOR Phase-Transitions , 2016, IJCAI.

[23]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[24]  Carsten Sinz,et al.  Towards an Optimal CNF Encoding of Boolean Cardinality Constraints , 2005, CP.

[25]  J. Walsh A Closed Set of Normal Orthogonal Functions , 1923 .

[26]  Kaile Su,et al.  Improving WalkSAT for Random k-Satisfiability Problem with k > 3 , 2013, AAAI.

[27]  Noam Nisan,et al.  Constant depth circuits, Fourier transform, and learnability , 1989, 30th Annual Symposium on Foundations of Computer Science.

[28]  Gil Kalai,et al.  A Fourier-theoretic perspective on the Condorcet paradox and Arrow's theorem , 2002, Adv. Appl. Math..

[29]  C.R. Edwards The Application of the Rademacher–Walsh Transform to Boolean Function Classification and Threshold Logic Synthesis , 1975, IEEE Transactions on Computers.

[30]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[31]  Bart Selman,et al.  Evidence for Invariants in Local Search , 1997, AAAI/IAAI.

[32]  Kuldeep S. Meel,et al.  Phase Transition Behavior of Cardinality and XOR Constraints , 2019, IJCAI.

[33]  Yann LeCun,et al.  The Loss Surfaces of Multilayer Networks , 2014, AISTATS.

[34]  Toby Walsh,et al.  Handbook of Satisfiability: Volume 185 Frontiers in Artificial Intelligence and Applications , 2009 .

[35]  Michael I. Jordan,et al.  Stochastic Gradient Descent Escapes Saddle Points Efficiently , 2019, ArXiv.

[36]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[37]  Karem A. Sakallah,et al.  Pueblo: A Hybrid Pseudo-Boolean SAT Solver , 2006, J. Satisf. Boolean Model. Comput..

[38]  Peter J. Stuckey,et al.  Core-Boosted Linear Search for Incomplete MaxSAT , 2019, CPAIOR.

[39]  Shmuel Safra,et al.  Threshold Phenomena and Influence, with Some Perspectives from Mathematics, Computer Science, and Economics , 2005 .

[40]  Niklas Sörensson,et al.  Translating Pseudo-Boolean Constraints into SAT , 2006, J. Satisf. Boolean Model. Comput..

[41]  James M. Crawford,et al.  The Minimal Disagreement Parity Problem as a Hard Satisfiability Problem , 1995 .

[42]  Stefano Ermon,et al.  Variable Elimination in the Fourier Domain , 2015, ICML.

[43]  Claude Castelluccia,et al.  Extending SAT Solvers to Cryptographic Problems , 2009, SAT.

[44]  Stefano Ermon,et al.  Beyond Parity Constraints: Fourier Analysis of Hash Functions for Inference , 2016, ICML.

[45]  Jakob Nordström,et al.  Divide and Conquer: Towards Faster Pseudo-Boolean Solving , 2018, IJCAI.

[46]  Randal E. Bryant Binary decision diagrams and beyond: enabling technologies for formal verification , 1995, ICCAD.

[47]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[48]  Jia Hui Liang,et al.  Machine Learning for SAT Solvers , 2018 .

[49]  Dominique de Werra,et al.  Graph coloring with cardinality constraints on the neighborhoods , 2009, Discret. Optim..

[50]  Curtis Bright,et al.  SAT Solvers and Computer Algebra Systems: A Powerful Combination for Mathematics , 2019, CASCON.

[51]  Jehoshua Bruck,et al.  Polynomial threshold functions, AC functions and spectrum norms , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[52]  Jesús A. De Loera,et al.  Computing infeasibility certificates for combinatorial problems through Hilbert's Nullstellensatz , 2011, J. Symb. Comput..

[53]  Thomas Stützle,et al.  SATLIB: An Online Resource for Research on SAT , 2000 .

[54]  Chu Min Li,et al.  Integrating Equivalency Reasoning into Davis-Putnam Procedure , 2000, AAAI/IAAI.

[55]  Joao Marques-Silva,et al.  GRASP: A Search Algorithm for Propositional Satisfiability , 1999, IEEE Trans. Computers.

[56]  Suku Nair,et al.  Efficient calculation of spectral coefficients and their applications , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[57]  Martin J. Wainwright,et al.  Using linear programming to Decode Binary linear codes , 2005, IEEE Transactions on Information Theory.

[58]  J. Moore,et al.  Boolean Function Matching using Walsh Spectral Decision Diagrams , 2006, 2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software.

[59]  Eugene Goldberg,et al.  BerkMin: A Fast and Robust Sat-Solver , 2002, Discret. Appl. Math..

[60]  Armin Biere,et al.  PicoSAT Essentials , 2008, J. Satisf. Boolean Model. Comput..

[61]  Adrian Balint,et al.  Improving Stochastic Local Search for SAT with a New Probability Distribution , 2010, SAT.

[62]  Nathan Linial,et al.  The influence of variables on Boolean functions , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[63]  Uwe Schöning,et al.  Choosing Probability Distributions for Stochastic Local Search and the Role of Make versus Break , 2012, SAT.

[64]  Avishay Tal,et al.  Tight bounds on The Fourier Spectrum of AC0 , 2017, Electron. Colloquium Comput. Complex..

[65]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[66]  Andrey Bogdanov,et al.  Biclique Cryptanalysis of the Full AES , 2011, ASIACRYPT.

[67]  Armin Biere Lingeling, Plingeling, PicoSAT and PrecoSAT at SAT Race 2010 , 2010 .

[68]  Alan J. Hu,et al.  SAT Modulo Monotonic Theories , 2014, AAAI.

[69]  Krzysztof Czarnecki,et al.  MathCheck: A Math Assistant via a Combination of Computer Algebra Systems and SAT Solvers , 2015, CADE.

[70]  Anastasios Kyrillidis,et al.  FourierSAT: A Fourier Expansion-Based Algebraic Framework for Solving Hybrid Boolean Constraints , 2019, AAAI.

[71]  Olivier Bailleux,et al.  Efficient CNF Encoding of Boolean Cardinality Constraints , 2003, CP.

[72]  Colin Wei,et al.  General Bounds on Satisfiability Thresholds for Random CSPs via Fourier Analysis , 2017, AAAI.

[73]  Rolf Drechsler,et al.  Spectral Techniques in VLSI CAD , 2001, Springer US.

[74]  Hans van Maaren,et al.  A two phase algorithm for solving a class of hard satissfiability problems , 1998 .