# Space-Time Interpolants

@inproceedings{Frehse2018SpaceTimeI, title={Space-Time Interpolants}, author={Goran Frehse and Mirco Giacobbe and Thomas A. Henzinger}, booktitle={CAV}, year={2018} }

Reachability analysis is difficult for hybrid automata with affine differential equations, because the reach set needs to be approximated. Promising abstraction techniques usually employ interval methods or template polyhedra. Interval methods account for dense time and guarantee soundness, and there are interval-based tools that overapproximate affine flowpipes. But interval methods impose bounded and rigid shapes, which make refinement expensive and fixpoint detection difficult. Template…

## 3 Citations

### Automatic time-unbounded reachability analysis of hybrid systems

- Computer Science
- 2019

This work develops methods for the polyhedral abstraction of hybrid automata, which construct coarse overapproximations and tightens them incrementally, in a CEGAR fashion, and introduces the first method for computing template directions from spurious counterexamples, so as to generalize and eliminate them.

### Verified Probabilistic Policies for Deep Reinforcement Learning

- Computer ScienceNFM
- 2022

This paper proposes an abstraction approach, based on interval Markov decision processes, that yields probabilistic guarantees on a policy’s execution, and presents techniques to build and solve these models using abstract interpretation, mixed-integer linear programming, entropy-based reﬁnement and Probabilistic model checking.

### Chemical Case Studies in KeYmaera X

- Computer ScienceFMICS
- 2022

This paper is the first to use a theorem-prover to verify hybrid chemical models: the KeYmaera X prover for differential dynamic logic, which provides parametric results that hold for a whole range of parameter values, non-linear physical dynamics, and a small trusted computing base.

## References

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This technique constructs over-approximations of the reachable states using template polyhedra so that operations used in symbolic model checking such as intersection, union and post-condition across discrete transitions over templatepolyhedra can be computed efficiently without requiring expensive vertex enumeration.

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This work presents a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples and embeds it inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible.

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We present a scalable reachability algorithm for hybrid systems with piecewise affine, non-deterministic dynamics. It combines polyhedra and support function representations of continuous sets to…

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This paper reduces the problem of detecting spurious transitions to the well-known problem of showing that two convex sets are disjoint by finding a hyperplane that separates them, and generalizes this to flowpipes by considering hyperplanes that evolve with time in correspondence to the dynamics of the system.

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A max-strategy improvement algorithm is used for computing an abstract semantics for affine hybrid automata that is based on template polyhedra and safely over-approximates the concrete semantics and shows that the corresponding abstract reachability problem is in co-NP.

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The notion of directional distance is introduced which is appropriate for measuring approximation effectiveness with respect to verifying a safety property and an implementation of the reachability algorithm is described which favors the constraint-based representation over the vertex-based one and avoids expensive conversions between them.

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This paper introduces iterative relaxation abstraction (IRA), a new method for reachability analysis of LHA that aims to improve scalability by combining the capabilities of current tools for…