Abstract
For the whole class of linear term rewriting systems, we define bottom-up rewriting which is a restriction of the usual notion of rewriting. We show that bottom-up rewriting effectively inverse-preserves recognizability and analyze the complexity of the underlying construction. The Bottom-Up class (BU) is, by definition, the set of linear systems for which every derivation can be replaced by a bottom-up derivation. Membership to BU turns out to be undecidable; we are thus lead to define more restricted classes: the classes SBU(k), k ∈ ℕ of Strongly Bottom-Up(k) systems for which we show that membership is decidable. We define the class of Strongly Bottom-Up systems by SBU = ∪ k ∈ ℕ SBU(k). We give a polynomial sufficient condition for a system to be in SBU. The class SBU contains (strictly) several classes of systems which were already known to inverse preserve recognizability.
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Durand, I., Sénizergues, G. (2007). Bottom-Up Rewriting Is Inverse Recognizability Preserving. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_10
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DOI: https://doi.org/10.1007/978-3-540-73449-9_10
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