Abstract
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.
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Boichut, Y., Dao, TBH., Murat, V. (2011). Characterizing Conclusive Approximations by Logical Formulae. In: Delzanno, G., Potapov, I. (eds) Reachability Problems. RP 2011. Lecture Notes in Computer Science, vol 6945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24288-5_8
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DOI: https://doi.org/10.1007/978-3-642-24288-5_8
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