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on Rewriting techniques and applications
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MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
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Journal of Symbolic Computation
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RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
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Electronic Notes in Theoretical Computer Science (ENTCS)
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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 = Uk∈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.