Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
MetiTarski: An Automatic Prover for the Elementary Functions
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
SAT Modulo ODE: A Direct SAT Approach to Hybrid Systems
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Combined Decision Techniques for the Existential Theory of the Reals
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Solving Non-linear Polynomial Arithmetic via SAT Modulo Linear Arithmetic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
CalCS: SMT solving for non-linear convex constraints
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
δ-complete decision procedures for satisfiability over the reals
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Delta-Decidability over the Reals
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Formalization of Bernstein Polynomials and Applications to Global Optimization
Journal of Automated Reasoning
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We describe the open-source tool dReal, an SMT solver for nonlinear formulas over the reals. The tool can handle various nonlinear real functions such as polynomials, trigonometric functions, exponential functions, etc. dReal implements the framework of δ-complete decision procedures: It returns either unsat or δ-sat on input formulas, where δ is a numerical error bound specified by the user. dReal also produces certificates of correctness for both δ-sat (a solution) and unsat answers (a proof of unsatisfiability).