Space-Time Interpolants

  title={Space-Time Interpolants},
  author={Goran Frehse and Mirco Giacobbe and Thomas A. Henzinger},
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… 

Automatic time-unbounded reachability analysis of hybrid systems

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

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

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.



Symbolic Model Checking of Hybrid Systems Using Template Polyhedra

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.

Counterexample-Guided Refinement of Template Polyhedra

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.

SpaceEx: Scalable Verification of Hybrid Systems

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

Eliminating spurious transitions in reachability with support functions

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.

Template-Based Unbounded Time Verification of Affine Hybrid Automata

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.

Using Redundant Constraints for Refinement

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.

PHAVer: algorithmic verification of hybrid systems past HyTech

  • Goran Frehse
  • Computer Science
    International Journal on Software Tools for Technology Transfer
  • 2007
This work addresses the main problems of HyTech with PHAVer, a new tool for the exact verification of safety properties of hybrid systems with piecewise constant bounds on the derivatives, so-called linear hybrid automata.

Taylor Model Flowpipe Construction for Non-linear Hybrid Systems

This paper provides techniques for handling the effect of discrete transitions on Taylor model flow pipe construction and explores various solutions based on two ideas: domain contraction and range over-approximation.

Assume–guarantee verification of nonlinear hybrid systems with Ariadne

This paper will show how the approximation capabilities of Ariadne can be used to verify complex hybrid systems, adopting an assume–guarantee reasoning approach.

Reachability for Linear Hybrid Automata Using Iterative Relaxation Abstraction

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