GRKLib: a Guaranteed Runge Kutta Library

Abstract. Verification algorithms for networks of nonlinear hybrid automata (HA) can aid understanding and controling of biological processes such as cardiac arrhythmia, formation of memory, and genetic regulation. We present an algorithm for over-approximating reach sets of networks of nonlinear HA which can be used for sound and relatively complete invariant checking. First, it uses automatically computed input-to-state discrepancy functions for the individual automata modules in the network A for constructing a low-dimensional model M. Simulations of both A and M are then used to compute the reach tubes for A. These techniques enable us to handle a challenging verification problem involving a network of cardiac cells, where each cell has four continuous variables and 29 locations. Our prototype tool can check bounded-time invariants for networks with 5 cells (20 continuous variables, 295 locations) typically in less than 15 minutes for up to reasonable time horizons. From the computed reach tubes we can infer biologically relevant properties of the network from a set of initial states.

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“…For a closed dynamical system A with an initial state v, validated ODE solvers [11,13,40] can compute a sequence of sets R 0 , . .…”

Section: Simulations Of Dynamical Systemsmentioning

confidence: 99%

Invariant Verification of Nonlinear Hybrid Automata Networks of Cardiac Cells

Huang

Fan

Mereacre

et al. 2014

Computer Aided Verification

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“…We consider both domains, as in [5] the abstraction function was not defined, by relying on a particular type of ODE solver [4]. For TSF, we also consider two different approaches: when the step width is constant and fixed, and when we automatically determine the steps distribution.…”

Section: Abstraction Of a Continuous Functionmentioning

confidence: 99%

Linear Approximation of Continuous Systems with Trapezoid Step Functions

Costantini

Ferrara

Cortesi

2012

Programming Languages and Systems

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Abstract. We introduce a novel abstract domain for the safe approximation of continuous functions in the context of abstract interpretationbased static analysis. The key-idea is to represent C 2 + functions by a finite sequence of trapezoids. In this way, we get a strictly more precise approximation of the actual values with respect to existing approaches in the literature. Experimental results underline the effectiveness of the approach in terms of both precision and efficiency.

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“…The mathematical behavior of Simulink models is given using guaranteed numerical integration algorithms [21,2] while the simulation behaviors is given by an abstraction of numerical integration algorithms with Taylor forms.…”

Section: Semantics Of Continuous-time Modelsmentioning

confidence: 99%

Abstract Simulation: A Static Analysis of Simulink Models

Chapoutot

Martel²

2009

2009 International Conference on Embedded Software and Systems

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Abstract. Simulink is one of the most widely used industrial tools to design embedded systems. Applying formal methods sooner in the cycle of development is an important industrial challenge in order to reduce the cost of bug fixing. In this article, we introduce a new method, called Abstract Simulation and based on abstract interpretation of Simulink models. Abstract Simulation uses several numerical domains such as a domain for Taylor forms or floating-point numbers with errors. These domains allow us to estimate errors introduced by numerical algorithms and by computations during simulations. As a result, our method makes it possible to validate numerical behaviors of embedded systems modeled in Simulink. A prototype has been implemented and experimental results are commented.

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GRKLib: a Guaranteed Runge Kutta Library

Cited by 37 publications

References 9 publications

Invariant Verification of Nonlinear Hybrid Automata Networks of Cardiac Cells

Invariant Verification of Nonlinear Hybrid Automata Networks of Cardiac Cells

Linear Approximation of Continuous Systems with Trapezoid Step Functions

Abstract Simulation: A Static Analysis of Simulink Models

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