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Reachability for Linear Hybrid Automata Using Iterative Relaxation Abstraction

  • Sumit K. Jha
  • Bruce H. Krogh
  • James E. Weimer
  • Edmund M. Clarke
Conference paper
  • 1.9k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4416)

Abstract

This paper introduces iterative relaxation abstraction (IRA), a new method for reachability analysis of LHA that aims to improve scalability by combining the capabilities of current tools for analysis of low-dimensional LHA with the power of linear programming (LP) for large numbers of constraints and variables. IRA is inspired by the success of counterexample guided abstraction refinement (CEGAR) techniques in verification of discrete systems. On each iteration, a low-dimensional LHA called a relaxation abstraction is constructed using a subset of the continuous variables from the original LHA. Hybrid system reachability analysis then generates a regular language called the discrete path abstraction containing all possible counterexamples (paths to the bad locations) in the relaxation abstraction. If the discrete path abstraction is non-empty, a particular counterexample is selected and LP infeasibility analysis determines if the counterexample is spurious using the constraints along the path from the original high-dimensional LHA. If the counterexample is spurious, LP techniques identify an irreducible infeasible subset (IIS) of constraints from which the set of continuous variables is selected for the the construction of the next relaxation abstraction. IRA stops if the discrete path abstraction is empty or a legitimate counterexample is found. The effectiveness of the approach is illustrated with an example.

Keywords

Model Check Hybrid System Linear Constraint Regular Language Hybrid Automaton 
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.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Sumit K. Jha
    • 1
  • Bruce H. Krogh
    • 2
  • James E. Weimer
    • 2
  • Edmund M. Clarke
    • 1
  1. 1.Computer Science Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213USA
  2. 2.ECE Department, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA15213USA

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