Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Verified Real Number Calculations: A Library for Interval Arithmetic
IEEE Transactions on Computers
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
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
An algebraic approach for the unsatisfiability of nonlinear constraints
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
The strategy challenge in SMT solving
Automated Reasoning and Mathematics
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Though decidable, the theory of real closed fields (RCF) is fundamentally infeasible. This is unfortunate, as automatic proof methods for nonlinear real arithmetic are crucially needed in both formalised mathematics and the verification of real-world cyber-physical systems. Consequently, many researchers have proposed fast, sound but incomplete RCF proof procedures which are useful in various practical applications. We show how such practically useful, sound but incomplete RCF proof methods may be systematically utilised in the context of a complete RCF proof method without sacrificing its completeness. In particular, we present an extension of the RCF quantifier elimination method Partial CAD (P-CAD) which uses incomplete ∃ RCF proof procedures to "short-circuit" expensive computations during the lifting phase of P-CAD. We present the theoretical framework and preliminary experiments arising from an implementation in our RCF proof tool RAHD.