Combining Widening and Acceleration in Linear Relation Analysis

  • Laure Gonnord
  • Nicolas Halbwachs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4134)


Linear Relation Analysis [CH78, Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be arbitrarily refined by delaying the application of widening, the analysis quickly becomes too expensive with the increase of delay. Previous attempts at improving the precision of widening are not completely satisfactory, since none of them is guaranteed to improve the precision of the result, and they can nevertheless increase the cost of the analysis. In this paper, we investigate an improvement of Linear Relation Analysis consisting in computing, when possible, the exact (abstract) effect of a loop. This technique is fully compatible with the use of widening, and whenever it applies, it improves both the precision and the performance of the analysis.


Convex Hull Abstract Interpretation Reachable State Hybrid Automaton Control Graph 
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-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Laure Gonnord
    • 1
  • Nicolas Halbwachs
    • 1
  1. 1.VérimagGrenobleFrance

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