Handbook of satisfiability
"Satisfiability (SAT) related topics have attracted researchers from various disciplines: logic, applied areas such as planning, scheduling, operations research and combinatorial optimization, but also theoretical issues on the theme of complexity and much more, they all are connected through S...
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| Hlavní autori: | , , , |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Amsterdam
IOS Press
2009
SAGE Publications, Limited IOS |
| Vydanie: | 1 |
| Edícia: | Frontiers in artificial intelligence and applications |
| Predmet: | |
| ISBN: | 1586039296, 9781586039295 |
| On-line prístup: | Získať plný text |
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- 24.3 Applications of QBFs and QBF reasoning -- 24.4 QBF solvers -- 24.5 Other approaches, extensions and conclusions -- References -- Chapter 25. SAT Techniques for Modal and Description Logics -- 25.1 Introduction -- 25.2 Background -- 25.3 Basic Modal DPLL -- 25.4 Advanced Modal DPLL -- 25.5 The OBDD-based Approach -- 25.6 The Eager DPLL-based approach -- References -- Chapter 26. Satisfiability Modulo Theories -- 26.1 Introduction -- 26.2 Background -- 26.3 Eager Encodings to SAT -- 26.4 Integrating Theory Solvers into SAT Engines -- 26.5 Theory Solvers -- 26.6 Combining Theories -- 26.7 Extensions and Enhancements -- References -- Chapter 27. Stochastic Boolean Satisfiability -- 27.1 Introduction -- 27.2 Definitions and Notation -- 27.3 Complexity of SSAT and Related Problems -- 27.4 Applications -- 27.5 Analytical Results -- 27.6 Algorithms and Empirical Results -- 27.7 Stochastic Constraint Programming -- 27.8 Future Directions -- References -- Subject Index -- Cited Author Index -- Contributing Authors and Affiliations
- 11.1 Introduction -- 11.2 Deficiency -- 11.3 Resolution and Homomorphism -- 11.4 Special Classes -- 11.5 Extension to non-clausal formulas -- 11.6 Minimal Falsity for QBF -- 11.7 Applications and Experimental Results -- 11.8 Generalising satisfying assignments through "autarkies -- 11.9 The autarky monoid -- 11.10 Finding and using autarkies -- 11.11 Autarky systems: Using weaker forms of autarkies -- 11.12 Connections to combinatorics -- 11.13 Generalisations and extensions of autarkies -- 11.14 Conclusion -- References -- Chapter 12. Worst-Case Upper Bounds -- 12.1 Preliminaries -- 12.2 Tractable and intractable classes -- 12.3 Upper bounds for k-SAT -- 12.4 Upper bounds for General SAT -- 12.5 How large is the exponent? -- 12.6 Summary table -- References -- Chapter 13. Fixed-Parameter Tractability -- 13.1 Introduction -- 13.2 Fixed-Parameter Algorithms -- 13.3 Parameterized SAT -- 13.4 Backdoor Sets -- 13.5 Treewidth -- 13.6 Matchings -- 13.7 Concluding Remarks -- References -- Part II. Applications and Extensions -- Chapter 14. Bounded Model Checking -- 14.1 Model Checking -- 14.2 Bounded Semantics -- 14.3 Propositional Encodings -- 14.4 Completeness -- 14.5 Induction -- 14.6 Interpolation -- 14.7 Completeness with Interpolation -- 14.8 Invariant Strengthening -- 14.9 Related Work -- 14.10 Conclusion -- References -- Chapter 15. Planning and SAT -- 15.1 Introduction -- 15.2 Notation -- 15.3 Sequential Plans -- 15.4 Parallel Plans -- 15.5 Finding a Satisfiable Formula -- 15.6 Improved SAT Solving for Planning -- 15.7 QBF and Planning with Nondeterministic Actions -- References -- Chapter 16. Software Verification -- 16.1 Programs use Bit-Vectors -- 16.2 Formal Models of Software -- 16.3 Turning Bit-Vector Arithmetic into CNF -- 16.4 Bounded Model Checking for Software -- 16.5 Predicate Abstraction using SAT -- 16.6 Conclusion -- References
- Title page -- Contents -- Part I. Theory and Algorithms -- Chapter 1. A History of Satisfiability -- 1.1 Preface: the concept of satisfiability -- 1.2 The ancients -- 1.3 The medieval period -- 1.4 The renaissance -- 1.5 The first logic machine -- 1.6 Boolean algebra -- 1.7 Frege, logicism, and quantification logic -- 1.8 Russell and Whitehead -- 1.9 G"odel's incompleteness theorem -- 1.10 Effective process and recursive functions -- 1.11 Herbrand's theorem -- 1.12 Model theory and Satisfiability -- 1.13 Completeness of first-order logic -- 1.14 Application of logic to circuits -- 1.15 Resolution -- 1.16 The complexity or resolution -- 1.17 Refinement of Resolution-Based SAT Solvers -- 1.18 Upper bounds -- 1.19 Classes of easy expressions -- 1.20 Binary Decision Diagrams -- 1.21 Probabilistic analysis: SAT algorithms -- 1.22 Probabilistic analysis: thresholds -- 1.23 Stochastic Local Search -- 1.24 Maximum Satisfiability -- 1.25 Nonlinear formulations -- 1.26 Pseudo-Boolean Forms -- 1.27 Quantified Boolean formulas -- References -- Chapter 2. CNF Encodings -- 2.1 Introduction -- 2.2 Transformation to CNF -- 2.3 Case studies -- 2.4 Desirable properties of CNF encodings -- 2.5 Conclusion -- References -- Chapter 3. Complete Algorithms -- 3.1 Introduction -- 3.2 Technical Preliminaries -- 3.3 Satisfiability by Existential Quantification -- 3.4 Satisfiability by Inference Rules -- 3.5 Satisfiability by Search: The DPLL Algorithm -- 3.6 Satisfiability by Combining Search and Inference -- 3.7 Conclusions -- References -- Chapter 4. CDCL Solvers -- 4.1 Introduction -- 4.2 Notation -- 4.3 Organization of CDCL Solvers -- 4.4 Conflict Analysis -- 4.5 Modern CDCL Solvers -- 4.6 Bibliographical and Historical Notes -- References -- Chapter 5. Look-Ahead Based SAT Solvers -- 5.1 Introduction -- 5.2 General and Historical Overview -- 5.3 Heuristics
- Chapter 17. Combinatorial Designs by SAT Solvers -- 17.1 Introduction -- 17.2 Quasigroup Problems -- 17.3 Ramsey and Van der Waerden Numbers -- 17.4 Covering Arrays -- 17.5 Steiner Systems -- 17.6 Mendelsohn Designs -- 17.7 Encoding Design Theory Problems -- 17.8 Conclusions and Open Problems -- References -- Chapter 18. Connections to Statistical Physics -- 18.1 Introduction -- 18.2 Phase Transitions: Basic Concepts and Illustration -- 18.3 Phase transitions in random CSPs -- 18.4 Local search algorithms -- 18.5 Decimation based algorithms -- 18.6 Conclusion -- References -- Chapter 19. MaxSAT -- 19.1 Introduction -- 19.2 Preliminaries -- 19.3 Branch and Bound Algorithms -- 19.4 Complete Inference in MaxSAT -- 19.5 Approximation Algorithms -- 19.6 Partial MaxSAT and Soft Constraints -- 19.7 Evaluations of MaxSAT Solvers -- 19.8 Conclusions -- References -- Chapter 20. Model Counting -- 20.1 Computational Complexity of Model Counting -- 20.2 Exact Model Counting -- 20.3 Approximate Model Counting -- 20.4 Conclusion -- References -- Chapter 21. Non-Clausal SAT and ATPG -- 21.1 Introduction -- 21.2 Basic Definitions -- 21.3 Satisfiability Checking for Boolean Circuits -- 21.4 Automatic Test Pattern Generation -- 21.5 Conclusions -- References -- Chapter 22. Pseudo-Boolean and Cardinality Constraints -- 22.1 Introduction -- 22.2 Basic Definitions -- 22.3 Decision Problem versus Optimization Problem -- 22.4 Expressive Power of Cardinality and Pseudo-Boolean Constraints -- 22.5 Inference Rules -- 22.6 Current Algorithms -- 22.7 Conclusion -- References -- Chapter 23. QBF Theory -- 23.1 Introduction -- 23.2 Syntax and Semantics -- 23.3 Complexity Results -- 23.4 Models and Expressive power -- 23.5 Q-Resolution -- 23.6 Quantified Horn Formulas and Q2-CNF -- References -- Chapter 24. QBFs reasoning -- 24.1 Introduction -- 24.2 Quantified Boolean Logic
- 5.4 Additional Reasoning -- 5.5 Eager Data-Structures -- References -- Chapter 6. Incomplete Algorithms -- 6.1 Greedy Search and Focused Random Walk -- 6.2 Extensions of the Basic Local Search Method -- 6.3 Discrete Lagrangian Methods -- 6.4 The Phase Transition Phenomenon in Random k-SAT -- 6.5 A New Technique for Random k-SAT: Survey Propagation -- 6.6 Conclusion -- References -- Chapter 7. Fundaments of Branching Heuristics -- 7.1 Introduction -- 7.2 A general framework for branching algorithms -- 7.3 Branching tuples and the canonical projection -- 7.4 Estimating tree sizes -- 7.5 Axiomatising the canonical order on branching tuples -- 7.6 Alternative projections for restricted branching width -- 7.7 How to select distances and measures -- 7.8 Optimising distance functions -- 7.9 The order of branches -- 7.10 Beyond clause-sets -- 7.11 Conclusion and outlook -- References -- Chapter 8. Random Satisfiability -- 8.1 Introduction -- 8.2 The State of the Art -- 8.3 Random MAX k-SAT -- 8.4 Physical Predictions for Solution-space Geometry -- 8.5 The Role of the Second Moment Method -- 8.6 Generative models -- 8.7 Algorithms -- 8.8 Belief/Survey Propagation and the Algorithmic Barrier -- 8.9 Backtracking Algorithms -- 8.10 Exponential Running-Time for k > -- 3 -- References -- Chapter 9. Exploiting Runtime Variation in Complete Solvers -- 9.1 Runtime Variation in Backtrack Search -- 9.2 Exploiting Runtime Variation: Randomization and Restarts -- 9.3 Conclusion -- References -- Chapter 10. Symmetry and Satisfiability -- 10.1 Motivating Example -- 10.2 Preliminaries -- 10.3 Group Theory Basics -- 10.4 CNF Symmetry -- 10.5 Automorphism Group of a Colored Graph -- 10.6 Symmetry Detection -- 10.7 Symmetry Breaking -- 10.8 Summary and a Look Forward -- 10.9 Bibliographic Notes -- References -- Chapter 11. Minimal Unsatisfiability and Autarkies