Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
The complexity of linear problems in fields
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Complexity of deciding Tarski algebra
Journal of Symbolic Computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Quantifier elimination for real algebra—the cubic case
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
REDLOG: computer algebra meets computer logic
ACM SIGSAM Bulletin
Nonlinear control system design by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Simplification of quantifier-free formulae over ordered fields
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Synthesizing Switching Logic Using Constraint Solving
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Variant real quantifier elimination: algorithm and application
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Switching logic synthesis for reachability
EMSOFT '10 Proceedings of the tenth ACM international conference on Embedded software
SOS methods for semi-algebraic games and optimization
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Efficient preprocessing methods for quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
Transcendental inductive invariants generation for non-linear differential and hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Timed relational abstractions for sampled data control systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
HybridSAL relational abstracter
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
On the limits of the classical approach to cost analysis
SAS'12 Proceedings of the 19th international conference on Static Analysis
Automated Reasoning and Mathematics
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
Time-aware relational abstractions for hybrid systems
Proceedings of the Eleventh ACM International Conference on Embedded Software
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We present the application of real quantifier elimination to formal verification and synthesis of continuous and switched dynamical systems. Through a series of case studies, we show how first-order formulas over the reals arise when formally analyzing models of complex control systems. Existing off-the-shelf quantifier elimination procedures are not successful in eliminating quantifiers from many of our benchmarks. We therefore automatically combine three established software components: virtual subtitution based quantifier elimination in Reduce/Redlog, cylindrical algebraic decomposition implemented in Qepcad, and the simplifier Slfq implemented on top of Qepcad. We use this combination to successfully analyze various models of systems including adaptive cruise control in automobiles, adaptive flight control system, and the classical inverted pendulum problem studied in control theory.