Strictly Orthogonal Left Linear Rewrite Systems and Primitive Recursion

Adam Cichon 1 Elias Tahhan-Bittar
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Let F be a signature and R a strictly orthogonal rewrite system on ground terms of F. We give an effective proof of a bounding condition for R, based on a detailed analysis of how terms are transformed during the rewrite process, which allows us to give recursive bounds on the derivation lengths of terms. We give a syntactic characterisation of the Grzegorczyk hierarchy and a rewriting schema for calculating its functions. As a consequence of this, using results of Elias Tahhan-Bittar, it can be shown that, for n > 2, the derivation length functions for functions in Grzegorczyk class En belong to Grzegorczyk class En+1. We also give recursive bounds for the derivation lengths of functions defined by parameter recursion.
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https://hal.inria.fr/inria-00098335
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Submitted on : Monday, September 25, 2006 - 3:36:08 PM
Last modification on : Thursday, January 11, 2018 - 6:19:48 AM

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Adam Cichon, Elias Tahhan-Bittar. Strictly Orthogonal Left Linear Rewrite Systems and Primitive Recursion. [Intern report] 98-R-351 || cichon98b, 1998, 16 p. ⟨inria-00098335⟩

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