Scalable Static Hybridization Methods for Analysis of Nonlinear Systems

Bak, Stanley; Bogomolov, Sergiy; Henzinger, Thomas A.; Johnson, Taylor T.; Prakash, Pradyot

doi:10.1145/2883817.2883837

Cited by 28 publications

(34 citation statements)

References 32 publications

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“…Ù Û Dynamics scaling can alter the set of states reachable with executions of a fixed duration, without altering the final (time-invariant) continuous reachable set. This is practically useful, because reachability algorithms usually perform their computations using sets which correspond to continuous trajectories of a fixed duration, which is sometimes called the currently-tracked set of states [8].…”

Section: Dynamics Scaling Transformationmentioning

confidence: 99%

“…Model transformations can be used to derive abstractions [14][15][16]28]. Bak et al [8] use model transformations to encode a hybridization process, i.e. reduction of the analysis of non-linear hybrid automata to linear ones, also using time-triggered transitions.…”

Section: Related Workmentioning

confidence: 99%

“…In particular, we leverage time-triggered transitions [2,8]. In a system with time-triggered transitions, the discrete mode change occurs after a certain amount of time has elapsed.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Bak

Bogomolov

Althoff

2017

Lecture Notes in Computer Science

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Abstract.A promising technique for the formal verification of embedded and cyber-physical systems is flow-pipe construction, which creates a sequence of regions covering all reachable states over time. Flow-pipe construction methods can check whether specifications are met for all states, rather than just testing using a finite and incomplete set of simulation traces. A fundamental challenge when using flow-pipe construction on high-dimensional systems is the cost of geometric operations, such as intersection and convex hull. We address this challenge by showing that it is often possible to remove the need to perform high-dimensional geometric operations by combining two model transformations, direct time-triggered conversion and dynamics scaling. Further, we prove the overapproximation error in the conversion can be made arbitrarily small. Finally, we show that our transformation-based approach enables the analysis of a drivetrain system with up to 51 dimensions.

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Section: Dynamics Scaling Transformationmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Bak

Bogomolov

Althoff

2017

Lecture Notes in Computer Science

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“…To put the existing related work in context, it is useful to consider several characteristics relating to the language considered and the transformation used, namely, whether the language is domain-specific (or general purpose), whether it supports equations, whether the transformation is done at compile-time (or runtime), whether the tool performs let-insertion (to avoid code duplication), whether the language is statically typed, and whether the tool provide accurate source level error reporting. The systems that we will consider are partial evaluation systems for C, namely, C-mix [16] and Tempo [10]; template instantiation mechanisms, namely, C++ Templates [11] and Template Haskell [27]; multi-stage programming languages, namely, MetaOCaml [11] and LMS [25]; the Verilog Preprocessor [26]; and the hybridization technique [4]. Table 1 provides an overview of how these different systems related to these key properties.…”

Section: Related Workmentioning

confidence: 99%

Compile-Time Extensions to Hybrid ODEs

Zeng

Bartha

Taha

2017

Electron. Proc. Theor. Comput. Sci.

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Reachability analysis for hybrid systems is an active area of development and has resulted in many promising prototype tools. Most of these tools allow users to express hybrid system as automata with a set of ordinary differential equations (ODEs) associated with each state, as well as rules for transitions between states. Significant effort goes into developing and verifying and correctly implementing those tools. As such, it is desirable to expand the scope of applicability tools of such as far as possible. With this goal, we show how compile-time transformations can be used to extend the basic hybrid ODE formalism traditionally supported in hybrid reachability tools such as SpaceEx or Flow*. The extension supports certain types of partial derivatives and equational constraints. These extensions allow users to express, among other things, the Euler-Lagrangian equation, and to capture practically relevant constraints that arise naturally in mechanical systems. Achieving this level of expressiveness requires using a binding time-analysis (BTA), program differentiation, symbolic Gaussian elimination, and abstract interpretation using interval analysis. Except for BTA, the other components are either readily available or can be easily added to most reachability tools. The paper therefore focuses on presenting both the declarative and algorithmic specifications for the BTA phase, and establishes the soundness of the algorithmic specifications with respect to the declarative one.

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“…In this setting, a given system is replaced by an abstraction where the system state space is partitioned and the original nonlinear dynamics is replaced with a simpler one in each induced partition. The resulting abstraction can either keep some approximated version of continuous dynamics [3,2] or reason in discrete terms only [19,20,18]. In the following, we consider discrete abstractions of hybrid systems.…”

Section: Introductionmentioning

confidence: 99%

Discrete Abstraction of Multiaffine Systems

Kong

Bartocci

Bogomolov

et al. 2016

Hybrid Systems Biology

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Abstract. Many biological systems can be modeled as multiane hybrid systems. Due to the nonlinearity of multiane systems, it is dicult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete abstraction signicantly determines the level of condence we can have in the properties of the original system. In this paper, in order to reduce the conservativeness of a discrete abstraction, we propose a new method based on a sucient and necessary decision condition for computing discrete transitions between states in the abstract system. We assume the state space partition of a multiane system to be based on a set of multivariate polynomials. Hence, a rectangular partition dened in terms of polynomials of the form (xi − c) is just a simple case of multivariate polynomial partition, and the new decision condition applies naturally. We analyze and demonstrate the improvement of our method over the existing methods using some examples.

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Scalable Static Hybridization Methods for Analysis of Nonlinear Systems

Cited by 28 publications

References 32 publications

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Time-Triggered Conversion of Guards for Reachability Analysis of Hybrid Automata

Compile-Time Extensions to Hybrid ODEs

Discrete Abstraction of Multiaffine Systems

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