@phdthesis{6894,
abstract = {Hybrid automata combine finite automata and dynamical systems, and model the interaction of digital with physical systems. Formal analysis that can guarantee the safety of all behaviors or rigorously witness failures, while unsolvable in general, has been tackled algorithmically using, e.g., abstraction, bounded model-checking, assisted theorem proving.
Nevertheless, very few methods have addressed the time-unbounded reachability analysis of hybrid automata and, for current sound and automatic tools, scalability remains critical. We develop methods for the polyhedral abstraction of hybrid automata, which construct coarse overapproximations and tightens them incrementally, in a CEGAR fashion. We use template polyhedra, i.e., polyhedra whose facets are normal to a given set of directions.
While, previously, directions were given by the user, we introduce (1) the first method
for computing template directions from spurious counterexamples, so as to generalize and
eliminate them. The method applies naturally to convex hybrid automata, i.e., hybrid
automata with (possibly non-linear) convex constraints on derivatives only, while for linear
ODE requires further abstraction. Specifically, we introduce (2) the conic abstractions,
which, partitioning the state space into appropriate (possibly non-uniform) cones, divide
curvy trajectories into relatively straight sections, suitable for polyhedral abstractions.
Finally, we introduce (3) space-time interpolation, which, combining interval arithmetic
and template refinement, computes appropriate (possibly non-uniform) time partitioning
and template directions along spurious trajectories, so as to eliminate them.
We obtain sound and automatic methods for the reachability analysis over dense
and unbounded time of convex hybrid automata and hybrid automata with linear ODE.
We build prototype tools and compare—favorably—our methods against the respective
state-of-the-art tools, on several benchmarks.},
author = {Giacobbe, Mirco},
issn = {2663-337X},
pages = {132},
publisher = {IST Austria},
title = {{Automatic time-unbounded reachability analysis of hybrid systems}},
doi = {10.15479/AT:ISTA:6894},
year = {2019},
}
@inproceedings{7453,
abstract = {We illustrate the ingredients of the state-of-the-art of model-based approach for the formal design and verification of cyber-physical systems. To capture the interaction between a discrete controller and its continuously evolving environment, we use the formal models of timed and hybrid automata. We explain the steps of modeling and verification in the tools Uppaal and SpaceEx using a case study based on a dual-chamber implantable pacemaker monitoring a human heart. We show how to design a model as a composition of components, how to construct models at varying levels of detail, how to establish that one model is an abstraction of another, how to specify correctness requirements using temporal logic, and how to verify that a model satisfies a logical requirement.},
author = {Alur, Rajeev and Giacobbe, Mirco and Henzinger, Thomas A and Larsen, Kim G. and Mikučionis, Marius},
booktitle = {Computing and Software Science},
isbn = {9783319919072},
issn = {0302-9743},
pages = {452--477},
publisher = {Springer Nature},
title = {{Continuous-time models for system design and analysis}},
doi = {10.1007/978-3-319-91908-9_22},
volume = {10000},
year = {2019},
}
@inproceedings{140,
abstract = {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 polyhedra, on the other hand, can be adapted flexibly and can be unbounded, but sound template refinement for unbounded reachability analysis has been implemented only for systems with piecewise constant dynamics. We capitalize on the advantages of both techniques, combining interval arithmetic and template polyhedra, using the former to abstract time and the latter to abstract space. During a CEGAR loop, whenever a spurious error trajectory is found, we compute additional space constraints and split time intervals, and use these space-time interpolants to eliminate the counterexample. Space-time interpolation offers a lazy, flexible framework for increasing precision while guaranteeing soundness, both for error avoidance and fixpoint detection. To the best of out knowledge, this is the first abstraction refinement scheme for the reachability analysis over unbounded and dense time of affine hybrid systems, which is both sound and automatic. We demonstrate the effectiveness of our algorithm with several benchmark examples, which cannot be handled by other tools.},
author = {Frehse, Goran and Giacobbe, Mirco and Henzinger, Thomas A},
issn = {03029743},
location = {Oxford, United Kingdom},
pages = {468 -- 486},
publisher = {Springer},
title = {{Space-time interpolants}},
doi = {10.1007/978-3-319-96145-3_25},
volume = {10981},
year = {2018},
}
@article{1351,
abstract = {The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives higher assurance and scalability. We focus on Wagner’s weighted GRN model with varying weights, which is used in evolutionary biology. In the model, weight parameters represent the gene interaction strength that may change due to genetic mutations. For a property of interest, we synthesise the constraints over the parameter space that represent the set of GRNs satisfying the property. We experimentally show that our parameter synthesis procedure computes the mutational robustness of GRNs—an important problem of interest in evolutionary biology—more efficiently than the classical simulation method. We specify the property in linear temporal logic. We employ symbolic bounded model checking and SMT solving to compute the space of GRNs that satisfy the property, which amounts to synthesizing a set of linear constraints on the weights.},
author = {Giacobbe, Mirco and Guet, Calin C and Gupta, Ashutosh and Henzinger, Thomas A and Paixao, Tiago and Petrov, Tatjana},
issn = {00015903},
journal = {Acta Informatica},
number = {8},
pages = {765 -- 787},
publisher = {Springer},
title = {{Model checking the evolution of gene regulatory networks}},
doi = {10.1007/s00236-016-0278-x},
volume = {54},
year = {2017},
}
@inproceedings{631,
abstract = {Template polyhedra generalize intervals and octagons to polyhedra whose facets are orthogonal to a given set of arbitrary directions. They have been employed in the abstract interpretation of programs and, with particular success, in the reachability analysis of hybrid automata. While previously, the choice of directions has been left to the user or a heuristic, we present a method for the automatic discovery of directions that generalize and eliminate spurious counterexamples. We show that for the class of convex hybrid automata, i.e., hybrid automata with (possibly nonlinear) convex constraints on derivatives, such directions always exist and can be found using convex optimization. We embed our method inside a CEGAR loop, thus enabling the time-unbounded reachability analysis of an important and richer class of hybrid automata than was previously possible. We evaluate our method on several benchmarks, demonstrating also its superior efficiency for the special case of linear hybrid automata.},
author = {Bogomolov, Sergiy and Frehse, Goran and Giacobbe, Mirco and Henzinger, Thomas A},
isbn = {978-366254576-8},
location = {Uppsala, Sweden},
pages = {589 -- 606},
publisher = {Springer},
title = {{Counterexample guided refinement of template polyhedra}},
doi = {10.1007/978-3-662-54577-5_34},
volume = {10205},
year = {2017},
}
@inproceedings{647,
abstract = {Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for the abstraction. In this paper, we propose an approach to constructing a new kind of abstraction called conic abstraction for affine hybrid systems, and to computing reachable sets based on this abstraction. The essential feature of a conic abstraction is that it partitions the state space of a system into a set of convex polyhedral cones which is derived from a uniform conic partition of the derivative space. Such a set of polyhedral cones is able to cut all trajectories of the system into almost straight segments so that every segment of a reach pipe in a polyhedral cone tends to be straight as well, and hence can be over-approximated tightly by polyhedra using similar techniques as HyTech or PHAVer. In particular, for diagonalizable affine systems, our approach can guarantee to find an invariant for unbounded reachable sets, which is beyond the capability of bounded-time reachability analysis tools. We implemented the approach in a tool and experiments on benchmarks show that our approach is more powerful than SpaceEx and PHAVer in dealing with diagonalizable systems.},
author = {Bogomolov, Sergiy and Giacobbe, Mirco and Henzinger, Thomas A and Kong, Hui},
isbn = {978-331965764-6},
location = {Berlin, Germany},
pages = {116 -- 132},
publisher = {Springer},
title = {{Conic abstractions for hybrid systems}},
doi = {10.1007/978-3-319-65765-3_7},
volume = {10419 },
year = {2017},
}
@inproceedings{1835,
abstract = {The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives higher assurance and scalability. We focus on Wagner’s weighted GRN model with varying weights, which is used in evolutionary biology. In the model, weight parameters represent the gene interaction strength that may change due to genetic mutations. For a property of interest, we synthesise the constraints over the parameter space that represent the set of GRNs satisfying the property. We experimentally show that our parameter synthesis procedure computes the mutational robustness of GRNs –an important problem of interest in evolutionary biology– more efficiently than the classical simulation method. We specify the property in linear temporal logics. We employ symbolic bounded model checking and SMT solving to compute the space of GRNs that satisfy the property, which amounts to synthesizing a set of linear constraints on the weights.},
author = {Giacobbe, Mirco and Guet, Calin C and Gupta, Ashutosh and Henzinger, Thomas A and Paixao, Tiago and Petrov, Tatjana},
location = {London, United Kingdom},
pages = {469 -- 483},
publisher = {Springer},
title = {{Model checking gene regulatory networks}},
doi = {10.1007/978-3-662-46681-0_47},
volume = {9035},
year = {2015},
}