Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Theoretical Computer Science
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A Note on Abstract Interpretation Strategies for Hybrid Automata
Hybrid Systems II
Reachability Analysis via Face Lifting
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
The Symbolic Approach to Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Hybrid Systems: Computation and Control: 7th International Workshop, Hscc 2004, Philadelphia, Pa, Usa, March 2004: Proceedings (Lecture Notes in Computer Science, 2993)
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and 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
Computing differential invariants of hybrid systems as fixedpoints
Formal Methods in System Design
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Symbolic model checking of hybrid systems using template polyhedra
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
Generating invariants for non-linear hybrid systems by linear algebraic methods
SAS'10 Proceedings of the 17th international conference on Static analysis
SIAM Journal on Control and Optimization
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Computing semi-algebraic invariants for polynomial dynamical systems
EMSOFT '11 Proceedings of the ninth ACM international conference on Embedded software
Fixed point iteration for computing the time elapse operator
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Transcendental inductive invariants generation for non-linear differential and hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Exercises in nonstandard static analysis of hybrid systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Hyperstream processing systems: nonstandard modeling of continuous-time signals
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Exponential-Condition-Based barrier certificate generation for safety verification of hybrid systems
CAV'13 Proceedings of the 25th international conference on Computer Aided Verification
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We present a powerful computational method for automatically generating polynomial invariants of hybrid systems with linear continuous dynamics. When restricted to linear continuous dynamical systems, our method generates a set of polynomial equations (algebraic set) that is the best such over-approximation of the reach set. This shows that the set of algebraic invariants of a linear system is computable. The extension to hybrid systems is achieved using the abstract interpretation framework over the lattice defined by algebraic sets. Algebraic sets are represented using canonical Gröbner bases and the lattice operations are effectively computed via appropriate Gröbner basis manipulations.