Efficient Solving of Large Arithmetic Constraint Systems with Complex Boolean Structure [electronic resource] : Proof Engines for the Analysis of Hybrid Discrete-Continuous Systems /
Herde, Christian.author.
Due to the growing use of more and more complex computerized systems in safety-critical applications, the formal verification of such systems is increasingly gaining importance. Many automatic and semi-automatic schemes for hardware and software verification ultimately rely on decision procedures for discharging the proof obligations generated during the verification process. Christian Herde deals with the development of such procedures, providing methods for efficiently solving formulae comprising complex Boolean combinations of linear, polynomial, and transcendental arithmetic constraints, involving thousands of Boolean-, integer-, and real-valued variables. Although aiming at providing tool support for the verification of hybrid discrete-continuous systems, most of the techniques he describes are general purpose and have applications in many other domains, like operations research, planning, software validation, and electronic design automation.
Description based upon print version of record.
Foreword; Acknowledgements; Abstract; Zusammenfassung; Contents; List of Figures; List of Tables; 1 Introduction; 1.1 Formal Verification Using Satisfiability Checking; 1.2 Bounded Model Checking of Hybrid Systems; 1.3 Solvers for Boolean Combinations of Numerical Constraints; 1.3.1 Constraint Solving in a Nutshell; 1.3.2 Contributions of the Thesis; 1.3.3 Structure; 1.3.4 Sources; 2 Hybrid Dynamical Systems; 2.1 Modeling Hybrid Systems with Hybrid Automata; 2.2 Predicative Encodings of Hybrid Automata; 2.2.1 A Basic Encoding Scheme; 2.2.2 Hybridization of Continuous Dynamics
2.2.3 Encoding Flows Using Taylor Expansions3 Extending DPLL for Pseudo-Boolean Constraints; 3.1 The Logics; 3.2 State of the Art in SAT Solving; 3.2.1 Conversion into CNF; 3.2.2 SAT Checkers for CNFs; 3.3 Optimizing DPLL-Based Pseudo-Boolean Solvers; 3.3.1 DPLL for Pseudo-Boolean Constraints; 3.3.2 Generalization of Lazy Clause Evaluation; 3.3.3 Learning in Presence of Pseudo-Boolean Constraints; 3.4 Benchmark Results; 3.5 Discussion; 4 Integration of DPLL-SAT and Linear Programming; 4.1 The Logics; 4.2 Lazy Approach to SMT; 4.3 SAT Modulo the Theory of Linear Arithmetic
4.3.1 Feasibility Check Using LP4.3.2 Extractions of Explanations; 4.3.3 Learning from Feasible LPs; 4.3.4 Putting It All Together: a Sample Run; 4.4 Optimizations for BMC; 4.5 Benchmark Results; 4.6 Discussion; 5 Integration of DPLL and Interval Constraint Solving; 5.1 The Logics; 5.2 Algorithmic Basis; 5.3 The ISAT Algorithm; 5.3.1 Definitional Translation into Conjunctive Form; 5.3.2 Split-and-Deduce Search; 5.3.3 Arithmetic Deduction Rules; 5.3.4 Correctness; 5.3.5 Algorithmic Enhancements; 5.3.6 Progress and Termination; 5.4 Benchmark Results; 5.4.1 Impact of Conflict-Driven Learning
5.4.2 Comparison to ABSOLVER5.4.3 Comparison to HYSAT-1; 5.5 Reachability Analysis with HYSAT-2: a Case Study; 5.5.1 ETCS Model; 5.5.2 Encoding into HySAT; 5.5.3 Results; 5.6 Discussion; 6 Conclusion; 6.1 Achievements; 6.2 Perspectives; 6.3 Final Thoughts; Bibliography; Index
Dissertation Universität Oldenburg, 2010.
Includes bibliographical references and index.
Due to the growing use of more and more complex computerized systems in safety-critical applications, the formal verification of such systems is increasingly gaining importance. Many automatic and semi-automatic schemes for hardware and software verification ultimately rely on decision procedures for discharging the proof obligations generated during the verification process. Christian Herde deals with the development of such procedures, providing methods for efficiently solving formulae comprising complex Boolean combinations of linear, polynomial, and transcendental arithmetic constraints, involving thousands of Boolean-, integer-, and real-valued variables. Although aiming at providing tool support for the verification of hybrid discrete-continuous systems, most of the techniques he describes are general purpose and have applications in many other domains, like operations research, planning, software validation, and electronic design automation.
Computers.
Computer science.
Theory of Computation.
Computer Science, general.