A complex example of a simplifying rewrite system
Identifieur interne : 000B71 ( PascalFrancis/Checkpoint ); précédent : 000B70; suivant : 000B72A complex example of a simplifying rewrite system
Auteurs : H. Touzet [France]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 1998.
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- Pascal (Inist)
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Abstract
For a string rewriting system, it is known that termination by a simplification ordering implies multiple recursive complexity. This theoretical upper bound is, however, far from having been reached by known examples of rewrite systems. All known methods used to establish termination by simplification yield a primitive recursive bound. Furthermore, the study of the order types of simplification orderings suggests that the recursive path ordering is, in a broad sense, a maximal simplification or-dering. This would imply that simplifying string rewrite systems cannot go beyond primitive recursion. Contradicting this intuition, we construct here a simplifying string rewriting system whose complexity is not primitive recursive. This leads to a new lower bound for the complexity of simplifying string rewriting systems.
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Touzet</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Loria - Université Nancy 2 BP 239</s1><s2>54506 Vandœuvre-lès-Nancy</s2><s3>FRA</s3><sZ>1 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno><imprint><date when="1998">1998</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Combinatorial optimization</term><term>Complexity class</term><term>Computer theory</term><term>Functional programming</term><term>Recursivity</term><term>Rewriting systems</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Informatique théorique</term><term>Optimisation combinatoire</term><term>Système réécriture</term><term>Programmation fonctionnelle</term><term>Classe complexité</term><term>Récursivité</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">For a string rewriting system, it is known that termination by a simplification ordering implies multiple recursive complexity. 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