New Reachability Algorithm Cuts Verification Steps with Property-Driven Time-Step Adaptation
Paper from Aalborg University and Uni Freiburg uses safety property to adapt time steps, outperforming prior methods.
Safety verification for continuous-time linear systems typically requires discretizing time and then performing forward reachability analysis. Existing algorithms use either a fixed time step or adapt based on approximation error relative to the continuous dynamics. This new work from Mikkel Bjørn and colleagues flips that approach: they adapt the time step based on the safety property itself. The algorithm picks the largest possible step such that it can still prove the system stays safe, dramatically cutting the total number of steps needed.
To make this scalable, the authors introduce key optimizations. They avoid repeatedly computing the matrix exponential during discretization, a major bottleneck, and carefully balance approximation errors from states and inputs. This allows the algorithm to use large time steps while maintaining only moderate approximation error. On the large-scale SLICOT benchmark suite, the new method consistently outperforms other state-of-the-art approaches, proving safety with far fewer computational steps. The work is set to appear at QEST+FORMATS 2026.
- Algorithm adapts time step based on safety property, not just approximation error, enabling larger steps.
- Optimizations avoid repeated calculation of matrix exponential, reducing computational overhead.
- Outperforms existing methods on the SLICOT benchmark suite, requiring far fewer steps for safety verification.
Why It Matters
Enables faster and more scalable safety verification for critical control systems, reducing computation time.