Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
A cluster-based cylindrical algebraic decomposition algorithm
Journal of Symbolic Computation
On mechanical quantifier elimination for elementary algebra and geometry
Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
On a modular algorithm for computing GCDs of polynomials over algebraic number fields
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Quantifier elimination for real algebra—the cubic case
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Approaches to parallel quantifier elimination
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Simplification of truth-invariant cylindrical algebraic decompositions
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Guaranteed solution formula construction
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Improved projection for CAD's of R3
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Symbolic-interval cooperation in constraint programming
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
On propagation of equational constraints in CAD-based quantifier elimination
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
Quantified constraints under perturbation
Journal of Symbolic Computation
A perspective on symbolic mathematical computing and artificial intelligence
Annals of Mathematics and Artificial Intelligence
Heuristic search and pruning in polynomial constraints satisfaction
Annals of Mathematics and Artificial Intelligence
Testing Positiveness of Polynomials
Journal of Automated Reasoning
A New Approach for Automatic Theorem Proving in Real Geometry
Journal of Automated Reasoning
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
Decidable Controller Synthesis for Classes of Linear Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Reach Set Computations Using Real Quantifier Elimination
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
Solving Geometric Problems with Real Quantifier Elimination
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Automated Discovering and Proving for Geometric Inequalities
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic
AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Continuous First-Order Constraint Satisfaction
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
A generic projection operator for partial cylindrical algebraic decomposition
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Computer algebra handbook
Non-linear loop invariant generation using Gröbner bases
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
A poly-algorithmic approach to simplifying elementary functions
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Efficient projection orders for CAD
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Mathematics and Computers in Simulation - Special issue: Applications of computer algebra in science, engineering, simulation and special software
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A procedure for proving special function inequalities involving a discrete parameter
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Stability analysis of biological systems with real solution classification
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Optimally-stable second-order accurate difference schemes for non-linear conservation laws in 3D
Applied Numerical Mathematics
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Representations and Strategies for Solving Spatial Problems with Diagrams
VLHCC '07 Proceedings of the IEEE Symposium on Visual Languages and Human-Centric Computing
Constructing invariants for hybrid systems
Formal Methods in System Design
DISCOVERER: a tool for solving semi-algebraic systems
ACM Communications in Computer Algebra
Compositional information flow security for concurrent programs
Journal of Computer Security
Symbolic optimization of algebraic functions
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Theoretical Computer Science
Program Verification by Using DISCOVERER
Verified Software: Theories, Tools, Experiments
Differential Dynamic Logic for Verifying Parametric Hybrid Systems
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Quantifier Elimination for Approximate Factorization of Linear Partial Differential Operators
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Combining Isabelle and QEPCAD-B in the Prover's Palette
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Developing a labelled object-relational constraint database architecture for the projection operator
Data & Knowledge Engineering
On delineability of varieties in CAD-based quantifier elimination with two equational constraints
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computing cylindrical algebraic decomposition via triangular decomposition
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Proceedings of the 2009 conference on Symbolic numeric computation
Computing differential invariants of hybrid systems as fixedpoints
Formal Methods in System Design
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Optimally-stable second-order accurate difference schemes for non-linear conservation laws in 3D
Applied Numerical Mathematics
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Journal of Symbolic Computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
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SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
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HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
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ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
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Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Black-box/white-box simplification and applications to quantifier elimination
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
When can we detect that a P-finite sequence is positive?
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Termination of linear programs with nonlinear constraints
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Visually Dynamic Presentation of Proofs in Plane Geometry
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Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Quantified differential dynamic logic for distributed hybrid systems
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
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CASC'10 Proceedings of the 12th international conference on Computer algebra in scientific computing
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CONTROL'07 Proceedings of the 3rd WSEAS/IASME international conference on Dynamical systems and control
Solution formulas for cubic equations without or with constraints
Journal of Symbolic Computation
Algebraic analysis on asymptotic stability of continuous dynamical systems
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Verification and synthesis using real quantifier elimination
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Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
CASC'11 Proceedings of the 13th international conference on Computer algebra in scientific computing
CLP(QS): a declarative spatial reasoning framework
COSIT'11 Proceedings of the 10th international conference on Spatial information theory
Mathematics and Computers in Simulation
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UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Safety verification of hybrid systems by constraint propagation based abstraction refinement
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Quantifier elimination for constraint logic programming
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Efficient preprocessing methods for quantifier elimination
CASC'06 Proceedings of the 9th international conference on Computer Algebra in Scientific Computing
An algorithm for computing the complete root classification of a parametric polynomial
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Quantifier elimination for quartics
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
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AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
Real root isolation of multi-exponential polynomials with application
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Variant quantifier elimination
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Algebraic analysis on asymptotic stability of switched hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Proceedings of the 27th Annual ACM Symposium on Applied Computing
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Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Speeding up cylindrical algebraic decomposition by gröbner bases
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Abstract partial cylindrical algebraic decomposition i: the lifting phase
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Integrating Systems around the User: Combining Isabelle, Maple, and QEPCAD in the Prover's Palette
Electronic Notes in Theoretical Computer Science (ENTCS)
Symbolic termination analysis of solvable loops
Journal of Symbolic Computation
Triangular decomposition of semi-algebraic systems
Journal of Symbolic Computation
ACM Communications in Computer Algebra
ACM Communications in Computer Algebra
Theoretical Computer Science
Cylindrical algebraic decompositions for boolean combinations
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Termination conditions for positivity proving procedures
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Discovering polynomial Lyapunov functions for continuous dynamical systems
Journal of Symbolic Computation
Optimising problem formulation for cylindrical algebraic decomposition
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Note: On the complexity of quantified linear systems
Theoretical Computer Science
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The Cylindrical Algebraic Decomposition method (CAD) decomposes R^r into regions over which given polynomials have constant signs. An important application of CAD is quantifier elimination in elementary algebra and geometry. In this paper we present a method which intermingles CAD construction with truth evaluation so that parts of the CAD are constructed only as needed to further truth evaluation and aborts CAD construction as soon as no more truth evaluation is needed. The truth evaluation utilizes in an essential way any quantifiers which are present and additionally takes account of atomic formulas from which some variables are absent. Preliminary observations show that the new method is always more efficient than the original, and often significantly more efficient.