ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Immler, Fabian; Althoff, Matthias; Chen, Xin; Fan, Chuchu; Frehse, Goran; Kochdumper, Niklas; Li, Yangge; Mitra, Sayan; Tomar, M. S.

doi:10.29007/mskf

Cited by 13 publications

(26 citation statements)

References 17 publications

(19 reference statements)

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“…The benchmark suite consists of 141 continuous safety verification problems, with 90 earlier problems [78] and 51 new ones, all drawn from the literature [5,15,18,21,26,28,30,32,33,36,41,42,50,69,76,89,90,91]. Some of the problems are drawn from papers that present and discuss properties of a system of ODEs without explicitly providing initial and safe conditions; in such cases, we design our own initial and safe sets based on the provided discussion.…”

Section: Benchmark Suitementioning

confidence: 99%

Pegasus: A Framework for Sound Continuous Invariant Generation

Sogokon

Mitsch

Tan

et al. 2019

Lecture Notes in Computer Science

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Continuous invariants are an important component in deductive verification of hybrid and continuous systems. Just like discrete invariants are used to reason about correctness in discrete systems without unrolling their loops forever, continuous invariants are used to reason about differential equations without having to solve them. Automatic generation of continuous invariants remains one of the biggest practical challenges to the automation of formal proofs of safety for hybrid systems. There are at present many disparate methods available for generating continuous invariants; however, this wealth of diverse techniques presents a number of challenges, with different methods having different strengths and weaknesses. To address some of these challenges, we develop Pegasus: an automatic continuous invariant generator which allows for combinations of various methods, and integrate it with the KeYmaera X theorem prover for hybrid systems. We describe some of the architectural aspects of this integration, comment on its methods and challenges, and present an experimental evaluation on a suite of benchmarks.1 An etymological note on naming conventions. The KeY [3] prover provided the foundation for developing KeYmaera [58], an interactive theorem prover for hybrid systems. The name KeYmaera was a pun on the Chimera, a hybrid monster from Classical Greek mythology. The tactic language of the new (aXiomatic) KeYmaera X prover [24] is called Bellerophon [23], after the hero who defeats the Chimera in the myth. In keeping with an established tradition, the invariant generation framework is called Pegasus because the aid of this winged horse was crucial to the hero Bellerophon in his feat.

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Section: Benchmark Suitementioning

confidence: 99%

Pegasus: A Framework for Sound Continuous Invariant Generation

Sogokon

Mitsch

Tan

et al. 2019

Lecture Notes in Computer Science

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“…Moreover, the initial conditions may not always be accurately known. A solution to address these uncertainties is to compute using intervals, hence to rely on interval-based integration tools [10,14,2,3,4,17] possibly with guaranteed arithmetic [5,8,13].…”

Section: Introductionmentioning

confidence: 99%

Interval-Based Simulation of Zélus IVPs using DynIbex

Brown

Pessaux

2020

Acta Cybern

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Modeling continuous-time dynamical systems is a complex task. Fortunately some dedicated programming languages exist to ease this work. Zélus is one such language that generates a simulation executable which can be used to study the behavior of the modeled system. However, such simulations cannot handle uncertainties on some parameters of the system. This makes it necessary to run multiple simulations to check that the system fulfills particular requirements (safety for instance) for all the values in the uncertainty ranges. Interval-based guaranteed integration methods provide a solution to this problem. The DynIbex library provides such methods but it requires a manual encoding of the system in a general purpose programming language (C++). This article presents an extension of the Zélus compiler to generate interval-based guaranteed simulations of IVPs using DynIbex. This extension is conservative since it does not break the existing compilation workflow.

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“…For example, CORA implements several algorithms for linear and nonlinear hybrid systems in MAT-LAB [1], and also offers a standalone set library focused on zonotopes, as well as a library for interval arithmetic. A subset of the algorithms from CORA have been implemented in C++ in the tools CORA/SX and SymReach, leading in some instances to a speedup of up to a factor of 3 [16]. A few tools are implemented in Python.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

JuliaReach

Bogomolov

Forets

Frehse

et al. 2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art algorithms for calculus with convex sets. The library offers both concrete and lazy set representations, where the latter stands for the ability to delay set computations until they are needed. The choice of the programming language Julia and the accompanying documentation of our toolbox allow researchers to easily translate set-based algorithms from mathematics to software in a platform-independent way, while achieving runtime performance that is comparable to statically compiled languages. Combining lazy operations in high dimensions and explicit computations in low dimensions, JuliaReach can be applied to solve complex, large-scale problems. CCS CONCEPTS• Security and privacy → Logic and verification;

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ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Cited by 13 publications

References 17 publications

Pegasus: A Framework for Sound Continuous Invariant Generation

Pegasus: A Framework for Sound Continuous Invariant Generation

Interval-Based Simulation of Zélus IVPs using DynIbex

JuliaReach

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