Theory and Applications of Satisfiability Testing – SAT 2013

In recent years there has been some progress in our understanding of the proof-search problem for very low-depth proof systems, e.g. proof systems that manipulate formulas of very low complexity such as clauses (i.e. resolution), DNF-formulas (i.e. R(k) systems), or polynomial inequalities (i.e. semi-algebraic proof systems). In this talk I will overview this progress. I will start with bounded-width resolution, whose specialized proof-search algorithm is as easy as uninteresting, but whose proof-search problem is unintentionally solved by certain versions of conflict-driven clause-learning algorithms with restarts. I will continue with R(k) systems, whose proof-search problem turned out to hide the complexity of certain two-player games of interest in the area of systems synthesis and verification. And I will close with bounded-degree semialgebraic proof systems, whose proof-search problem turned out to hide the complexity of systems of linear equations over finite fields, among

[1]  Fahiem Bacchus,et al.  Solving MAXSAT by Solving a Sequence of Simpler SAT Instances , 2011, CP.

[2]  Cesare Tinelli,et al.  Satisfiability Modulo Theories , 2021, Handbook of Satisfiability.

[3]  Inês Lynce,et al.  A branch and bound algorithm for extracting smallest minimal unsatisfiable subformulas , 2008, Constraints.

[4]  Cesare Tinelli,et al.  Splitting on Demand in SAT Modulo Theories , 2006, LPAR.

[5]  Sharad Malik,et al.  On Solving the Partial MAX-SAT Problem , 2006, SAT.

[6]  Joao Marques-Silva,et al.  Improvements to Core-Guided Binary Search for MaxSAT , 2012, SAT.

[7]  Sharad Malik,et al.  Validating the result of a quantified Boolean formula (QBF) solver: theory and practice , 2005, Proceedings of the ASP-DAC 2005. Asia and South Pacific Design Automation Conference, 2005..

[8]  Inês Lynce,et al.  On Computing Minimum Unsatisfiable Cores , 2004, SAT.

[9]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[10]  Karem A. Sakallah,et al.  Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints , 2007, Journal of Automated Reasoning.

[11]  Maria Luisa Bonet,et al.  SAT-based MaxSAT algorithms , 2013, Artif. Intell..

[12]  Albert Oliveras,et al.  MiniMaxSAT: An Efficient Weighted Max-SAT solver , 2008, J. Artif. Intell. Res..

[13]  Carlos Ansótegui,et al.  Satisfiability Modulo Theories: An Efficient Approach for the Resource-Constrained Project Scheduling Problem , 2011, SARA.

[14]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[15]  Vasco M. Manquinho,et al.  Algorithms for Weighted Boolean Optimization , 2009, SAT.

[16]  Marco Bozzano,et al.  Efficient theory combination via boolean search , 2006, Inf. Comput..

[17]  Alberto Griggio,et al.  The MathSAT 5 SMT Solver ⋆ , 2012 .

[18]  Alberto Griggio,et al.  A Modular Approach to MaxSAT Modulo Theories , 2013, SAT.

[19]  Wolfgang Küchlin,et al.  Formal methods for the validation of automotive product configuration data , 2003, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[20]  Karem A. Sakallah,et al.  On Finding All Minimally Unsatisfiable Subformulas , 2005, SAT.

[21]  Felip Manyà,et al.  New Inference Rules for Max-SAT , 2007, J. Artif. Intell. Res..

[22]  Albert Oliveras,et al.  On SAT Modulo Theories and Optimization Problems , 2006, SAT.

[23]  Carlos Ansótegui,et al.  Solving weighted CSPs with meta-constraints by reformulation into satisfiability modulo theories , 2012, Constraints.

[24]  Alberto Griggio,et al.  Satisfiability Modulo the Theory of Costs: Foundations and Applications , 2010, TACAS.

[25]  Felip Manyà,et al.  MaxSAT, Hard and Soft Constraints , 2021, Handbook of Satisfiability.

[26]  M. Schaefer,et al.  Completeness in the Polynomial-Time Hierarchy A Compendium ∗ , 2008 .

[27]  Inês Lynce,et al.  A Branch-and-Bound Algorithm for Extracting Smallest Minimal Unsatisfiable Formulas , 2005, SAT.

[28]  Joao Marques-Silva,et al.  Core-Guided Binary Search Algorithms for Maximum Satisfiability , 2011, AAAI.

[29]  Armin Biere,et al.  Resolution-Based Certificate Extraction for QBF - (Tool Presentation) , 2012, SAT.

[30]  Alberto Griggio,et al.  A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories , 2007, SAT.

[31]  João P. Marques Silva.  Minimal Unsatisfiability: Models, Algorithms and Applications (Invited Paper). , 2010, ISMVL 2010.