Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Theoretical Computer Science
Symbolic model checking for real-time systems
Information and Computation
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
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
Robust multi-objective feedback design by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Testing stability by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
Deciding linear-trigonometric problems
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Proceedings of the International Workshop on Hybrid and Real-Time Systems
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
TACAS '95 Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Reachability Analysis via Face Lifting
HSCC '98 Proceedings of the First International Workshop on Hybrid Systems: Computation and Control
STeP: Deductive-Algorithmic Verification of Reactive and Real-Time Systems
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Reachability Analysis of Delta-NotchLateral Inhibition Using Predicate Abstraction
HiPC '02 Proceedings of the 9th International Conference on High Performance Computing
Hierarchical Hybrid Modeling of Embedded Systems
EMSOFT '01 Proceedings of the First International Workshop on Embedded Software
Mode Switching Synthesis for Reachability Specifications
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
SPeeDI - A Verification Tool for Polygonal Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Algorithmic analysis of polygonal hybrid systems, part I: Reachability
Theoretical Computer Science
Sampling-based Algorithm for Testing and Validating Robot Controllers
International Journal of Robotics Research
Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools
Theoretical Computer Science
Abstractions for hybrid systems
Formal Methods in System Design
Constructing invariants for hybrid systems
Formal Methods in System Design
Program Verification by Using DISCOVERER
Verified Software: Theories, Tools, Experiments
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Inclusion dynamics hybrid automata
Information and Computation
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions
Journal of Automated Reasoning
Span-reachability and observability of bilinear hybrid systems
Automatica (Journal of IFAC)
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Algebraic systems biology: theses and hypotheses
AB'07 Proceedings of the 2nd international conference on Algebraic biology
Reachable set computation for uncertain time-varying linear systems
Proceedings of the 14th international conference on Hybrid systems: computation and control
Verification and synthesis using real quantifier elimination
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Computing semi-algebraic invariants for polynomial dynamical systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
Behavioural approximations for restricted linear differential hybrid automata
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Observability of hybrid automata by abstraction
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Fixed point iteration for computing the time elapse operator
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
On the computational power of timed differentiable petri nets
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Static analysis for state-space reduction of polygonal hybrid systems
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
A compositional algorithm for parallel model checking of polygonal hybrid systems
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Refining the undecidability frontier of hybrid automata
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Primal–dual tests for safety and reachability
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Interrupt Timed Automata: verification and expressiveness
Formal Methods in System Design
Real root isolation of multi-exponential polynomials with application
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Triangular decomposition of semi-algebraic systems
Journal of Symbolic Computation
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Safety verification for linear systems
Proceedings of the Eleventh ACM International Conference on Embedded Software
Time-aware relational abstractions for hybrid systems
Proceedings of the Eleventh ACM International Conference on Embedded Software
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The control paradigm of physical processes being supervised by digital programs has lead to the development of a theory of hybrid systems combining finite state automata with differential equations. One of the most important problems in the verification of hybrid systems is the reachability problem. Even though the computation of reachable spaces for finite state machines is well developed, computing the reachable space of a differential equation is difficult. In this paper, we present the first known families of linear differential equations with a decidable reachability problem. This is achieved by posing the reachability computation as a quantifier elimination problem in the decidable theory of the reals. We illustrate the applicability of our approach by performing computations using the packages REDLOG and QEPCAD. Such symbolic computations can be incorporated in computer-aided verification tools for purely discrete systems, resulting in verification tools for hybrid systems with linear differential equations.