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Relational Abstractions for Continuous and Hybrid Systems

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6806)

Abstract

In this paper, we define relational abstractions of hybrid systems. A relational abstraction is obtained by replacing the continuous dynamics in each mode by a binary transition relation that relates a state of the system to any state that can potentially be reached at some future time instant using the continuous dynamics. We construct relational abstractions by reusing template-based invariant generation techniques for continuous systems described by Ordinary Differential Equations (ODE). As a result, we abstract a given hybrid system as a purely discrete, infinite-state system. We apply k-induction to this abstraction to prove safety properties, and use bounded model-checking to find potential falsifications. We present the basic underpinnings of our approach and demonstrate its use on many benchmark systems to derive simple and usable abstractions.

Keywords

  • Model Check
  • Hybrid System
  • Continuous System
  • Relational Invariant
  • Discrete Transition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sankaranarayanan’s work has been supported by NSF Career grant CNS-0953941. Tiwari’s work supported in part by DARPA under Contract No. FA8650-10-C-7078, NSF grants CSR-0917398 and SHF:CSR-1017483.

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Sankaranarayanan, S., Tiwari, A. (2011). Relational Abstractions for Continuous and Hybrid Systems. In: Gopalakrishnan, G., Qadeer, S. (eds) Computer Aided Verification. CAV 2011. Lecture Notes in Computer Science, vol 6806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22110-1_56

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  • DOI: https://doi.org/10.1007/978-3-642-22110-1_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22109-5

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