Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
“Sometimes” and “not never” revisited: on branching versus linear time temporal logic
Journal of the ACM (JACM) - The MIT Press scientific computation series
Differential automata and their discrete simulators
Non-Linear Analysis
Differential-algebraic equations index transformations
SIAM Journal on Scientific and Statistical Computing - Telecommunication Programs at U.S. Universities
The complexity of linear problems in fields
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Solving systems of polynomial inequalities in subexponential time
Journal of Symbolic Computation
Complexity of deciding Tarski algebra
Journal of Symbolic Computation
Some aspects of complexity in real algebraic geometry
Journal of Symbolic Computation
Quantifier elimination and the sign variation method for real root isolation
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Differential equations and dynamical systems
Differential equations and dynamical systems
Handbook of theoretical computer science (vol. B)
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Journal of Symbolic Computation
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Handbook of logic in computer science (vol. 2)
A classical mind
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Universal computation and other capabilities of hybrid and continuous dynamical systems
Theoretical Computer Science - Special issue on hybrid systems
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
General hybrid dynamical systems: modeling, analysis, and control
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
A formal description of hybrid systems
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Studies in hybrid systems: modeling, analysis, and control
Studies in hybrid systems: modeling, analysis, and control
A survey of the Theorema project
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Complexity and real computation
Complexity and real computation
First-order modal logic
Journal of the ACM (JACM)
Model checking
Proving termination with multiset orderings
Communications of the ACM
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Theoretical Computer Science
First-Order Dynamic Logic
Dynamic Logic
Process logic: preliminary report
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Analytica – An Experiment in Combining Theorem Proving and Symbolic Computation
Journal of Automated Reasoning
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
Automatic Symbolic Verification of Embedded Systems
IEEE Transactions on Software Engineering
Cooperation of Background Reasoners in Theory Reasoning by Residue Sharing
Journal of Automated Reasoning
Theoretical Computer Science
Hybrid Systems
Computer Algebra Meets Automated Theorem Proving: Integrating Maple and PVS
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An Extended Duration Calculus for Hybrid Real-Time Systems
Hybrid Systems
HYTECH: The Cornell HYbrid TECHnology Tool
Hybrid Systems II
On Hybrid Systems and the Modal µ-calculus
Hybrid Systems V
Deductive Verification of Hybrid Systems Using STeP
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
A New Class of Decidable Hybrid Systems
HSCC '99 Proceedings of the Second 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
Deduction in the Verification Support Environment (VSE)
FME '96 Proceedings of the Third International Symposium of Formal Methods Europe on Industrial Benefit and Advances in Formal Methods
Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
A Sequent Calculus for First-Order Dynamic Logic with Trace Modalities
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Incremental Closure of Free Variable Tableaux
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A Deductive Proof System for CTL
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
Parallel Real Root Isolation Using the Coefficient Sign Variation Method
Proceedings of the Second International Workshop on Computer Algebra and Parallelism
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
Modelling Free Flight with Collision Avoidance
ICECCS '01 Proceedings of the Seventh International Conference on Engineering of Complex Computer Systems
Verification of Hybrid Systems: Formalization and Proof Rules in PVS
ICECCS '01 Proceedings of the Seventh International Conference on Engineering of Complex Computer Systems
Logic for Computable Functions: description of a machine implementation.
Logic for Computable Functions: description of a machine implementation.
Journal of Automated Reasoning
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Convex Optimization
Model Checking Data-Dependent Real-Time Properties of the European Train Control System
FMCAD '06 Proceedings of the Formal Methods in Computer Aided Design
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Automated Technology for Verification and Analysis: Third International Symposium, ATVA 2005, Taipei, Taiwan, October 4-7, 2005, Proceedings (Lecture Notes in Computer Science)
Hybrid Systems: Computation and Control: 8th International Workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005, Proceedings (Lecture Notes in Computer Science)
Towards a Hybrid Dynamic Logic for Hybrid Dynamic Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
SAT-based Abstraction Refinement for Real-time Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
The complexity of quantifier elimination and cylindrical algebraic decomposition
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Semantical consideration on floyo-hoare logic
SFCS '76 Proceedings of the 17th Annual Symposium on Foundations of Computer Science
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Differential Dynamic Logic for Hybrid Systems
Journal of Automated Reasoning
A Temporal Dynamic Logic for Verifying Hybrid System Invariants
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
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
The KeY system 1.0 (Deduction Component)
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Logical Verification and Systematic Parametric Analysis in Train Control
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Computing Differential Invariants of Hybrid Systems as Fixedpoints
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Proceedings of the 4th international joint conference on Automated Reasoning
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
KeYmaera: A Hybrid Theorem Prover for Hybrid Systems (System Description)
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Information and Computation
Differential-algebraic Dynamic Logic for Differential-algebraic Programs
Journal of Logic and Computation
Proceedings of the 10th international conference on Hybrid systems: computation and control
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Model checking genetic regulatory networks with parameter uncertainty
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Systematic simulation using sensitivity analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
The image computation problem in hybrid systems model checking
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Differential logic for reasoning about hybrid systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Proceedings of the 6th international conference on Hybrid systems: computation and control
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Reachability analysis of nonlinear systems using conservative approximation
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Formal verification of an optimal air traffic conflict resolution and recovery algorithm
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Verifying nonlinear real formulas via sums of squares
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Automating verification of cooperation, control, and design in traffic applications
Formal methods and hybrid real-time systems
Verification of object-oriented software: The KeY approach
Verification of object-oriented software: The KeY approach
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Logical analysis of hybrid systems: a complete answer to a complexity challenge
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
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Hybrid systems are models for complex physical systems and are defined as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. With the goal of developing a theoretical and practical foundation for deductive verification of hybrid systems, we introduce differential dynamic logic as a new logic with which correctness properties of hybrid systems with parameterized system dynamics can be specified and verified naturally. As a verification technique that is suitable for automation, we introduce a free variable proof calculus with a novel combination of real-valued free variables and Skolemisation for lifting quantifier elimination for real arithmetic to dynamic logic. The calculus is compositional, i.e., it reduces properties of hybrid systems successively to properties of their parts. Our main result proves that this calculus axiomatises the transition behaviour of hybrid systems completely relative to differential equations. Systematically, we develop automated theorem proving techniques for our calculus and present proof procedures to tackle the complexities of integrating decision procedures for real arithmetic. For our logic, we further complement discrete induction with differential induction as a new continuous generalization of induction, with which hybrid systems can be verified by exploiting their differential constraints algebraically without having to solve them. Finally, we develop a fixedpoint algorithm for computing the differential invariants required for differential induction, and we introduce a differential saturation procedure that refines the system dynamics successively with differential invariants until correctness becomes provable. As a systematic combination of logic-based techniques, we obtain a sound verification procedure that is particularly suitable for parametric hybrid systems. We demonstrate our approch by verifying safety, controllability, liveness, and collision avoidance properties in case studies ranging from train control applications in the European Train Control System to air traffic control, where we prove collision avoidance in aircraft roundabout maneuvers.