Characterizing Conclusive Approximations by Logical Formulae

  • Yohan Boichut
  • Thi-Bich-Hanh Dao
  • Valérie Murat
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6945)


Considering an initial set of terms E, a rewriting relation \(\mathcal{R}\) and a goal set of terms Bad, reachability analysis in term rewriting tries to answer to the following question: does there exists at least one term of Bad that can be reached from E using the rewriting relation \(\mathcal{R}\)?

Some of the approaches try to show that there exists at least one term of Bad reachable from E using the rewriting relation \(\mathcal{R}\) by computing the set of reachable terms. Some others tackle the unreachability problem i.e. no term of Bad is reachable by rewriting from E. For the latter, over-approximations are computed. A main obstacle is to be able to compute an over-approximation precise enough that does not intersect Bad i.e. a conclusive approximation. This notion of precision is often defined by a very technical parameter of techniques implementing this over-approximation approach. In this paper, we propose a new characterization of conclusive approximations by logical formulae generated from a new kind of automata called symbolic tree automata. Solving a such formula leads automatically to a conclusive approximation without extra technical parameters.


Equivalence Class Logical Formula Horn Clause Symbolic State Reachability Analysis 
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 2011

Authors and Affiliations

  • Yohan Boichut
    • 1
  • Thi-Bich-Hanh Dao
    • 1
  • Valérie Murat
    • 2
  1. 1.LIFO - Université OrléansFrance
  2. 2.IRISA - Université Rennes 1France

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