Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
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
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Polyhedral Analysis for Synchronous Languages
SAS '99 Proceedings of the 6th International Symposium on Static Analysis
Algorithmic Analysis of Nonlinear Hybrid Systems
Proceedings of the 7th International Conference on Computer Aided Verification
The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Constructing invariants for hybrid systems
Formal Methods in System Design
Precise widening operators for convex polyhedra
SAS'03 Proceedings of the 10th international conference on Static analysis
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
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
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Automatic invariant generation for hybrid systems using ideal fixed points
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Verification constraint problems with strengthening
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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We investigate techniques for automatically generating symbolic approximations to the time solution of a system of differential equations. This is an important primitive operation for the safety analysis of continuous and hybrid systems. In this paper we design a time elapse operator that computes a symbolic over-approximation of time solutions to a continuous system starting from a given initial region. Our approach is iterative over the cone of functions (drawn from a suitable universe) that are non negative over the initial region. At each stage, we iteratively remove functions from the cone whose Lie derivatives do not lie inside the current iterate. If the iteration converges, the set of states defined by the final iterate is shown to contain all the time successors of the initial region. The convergence of the iteration can be forced using abstract interpretation operations such as widening and narrowing. We instantiate our technique to linear hybrid systems with piecewise-affine dynamics to compute polyhedral approximations to the time successors. Using our prototype implementation TimePass, we demonstrate the performance of our technique on benchmark examples.