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Abstract: Several types of term rewriting systems can be distinguished by the way theirrules overlap. In particular, we define the classes of prefix, suffix,bottom-up and top-down systems, which generalize similar classes on words. Ouraim is to study the derivation relation of such systems (i.e. the reflexive andtransitive closure of their rewriting relation) and, if possible, to provide afinite mechanism characterizing it. Using a notion of rational relations basedon finite graph grammars, we show that the derivation of any bottom-up,top-down or suffix systems is rational, while it can be non recursive forprefix systems.



Author: Antoine Meyer (LIAFA)

Source: https://arxiv.org/



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