Encoding the Hydra battle as a rewrite system
Identifieur interne :
000C82 ( PascalFrancis/Curation );
précédent :
000C81;
suivant :
000C83
Encoding the Hydra battle as a rewrite system
Auteurs : H. Touzet [
France]
Source :
-
Lecture notes in computer science [ 0302-9743 ] ; 1998.
RBID : Pascal:98-0427349
Descripteurs français
English descriptors
Abstract
In rewriting theory, termination of a rewrite system by Kruskal's theorem implies a theoretical upper bound on the complexity of the system. This bound is, however, far from having been reached by known examples of rewrite systems. All known orderings used to establish termination by Kruskal's theorem yield a multiply recursive bound. Furthermore, the study of the order types of such orderings suggests that the class of multiple recursive functions constitutes the least upper bound. Contradicting this intuition, we construct here a rewrite system which reduces by Kruskal's theorem and whose complexity is not multiply recursive. This system is even totally terminating. This leads to a new lower bound for the complexity of totally terminating rewrite systems and rewrite systems which reduce by Kruskal's theorem. Our construction relies on the Hydra battle using classical tools from ordinal theory and subrecursive functions.
| pA |
| A01 | 01 | 1 | | @0 0302-9743 |
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| A05 | | | | @2 1450 |
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| A08 | 01 | 1 | ENG | @1 Encoding the Hydra battle as a rewrite system |
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| A09 | 01 | 1 | ENG | @1 MFCS'98 : mathematical foundations of computer science 1998 : Brno, 24-28 August 1998 |
|---|
| A11 | 01 | 1 | | @1 TOUZET (H.) |
|---|
| A12 | 01 | 1 | | @1 BRIM (Lubos) @9 ed. |
|---|
| A12 | 02 | 1 | | @1 GRUSKA (Josef) @9 ed. |
|---|
| A12 | 03 | 1 | | @1 ZLATUSKA (Jirí) @9 ed. |
|---|
| A14 | 01 | | | @1 Loria -, Université Nancy 2, BP 239 @2 54506 Vandœuvre-lès-Nancy @3 FRA @Z 1 aut. |
|---|
| A20 | | | | @1 267-276 |
|---|
| A21 | | | | @1 1998 |
|---|
| A23 | 01 | | | @0 ENG |
|---|
| A26 | 01 | | | @0 3-540-64827-5 |
|---|
| A43 | 01 | | | @1 INIST @2 16343 @5 354000070098310230 |
|---|
| A44 | | | | @0 0000 @1 © 1998 INIST-CNRS. All rights reserved. |
|---|
| A45 | | | | @0 12 ref. |
|---|
| A47 | 01 | 1 | | @0 98-0427349 |
|---|
| A60 | | | | @1 P @2 C |
|---|
| A61 | | | | @0 A |
|---|
| A64 | | 1 | | @0 Lecture notes in computer science |
|---|
| A66 | 01 | | | @0 DEU |
|---|
| A66 | 02 | | | @0 USA |
|---|
| C01 | 01 | | ENG | @0 In rewriting theory, termination of a rewrite system by Kruskal's theorem implies a theoretical upper bound on the complexity of the system. This bound is, however, far from having been reached by known examples of rewrite systems. All known orderings used to establish termination by Kruskal's theorem yield a multiply recursive bound. Furthermore, the study of the order types of such orderings suggests that the class of multiple recursive functions constitutes the least upper bound. Contradicting this intuition, we construct here a rewrite system which reduces by Kruskal's theorem and whose complexity is not multiply recursive. This system is even totally terminating. This leads to a new lower bound for the complexity of totally terminating rewrite systems and rewrite systems which reduce by Kruskal's theorem. Our construction relies on the Hydra battle using classical tools from ordinal theory and subrecursive functions. |
|---|
| C02 | 01 | X | | @0 001D02A02 |
|---|
| C03 | 01 | X | FRE | @0 Informatique théorique @5 01 |
|---|
| C03 | 01 | X | ENG | @0 Computer theory @5 01 |
|---|
| C03 | 01 | X | SPA | @0 Informática teórica @5 01 |
|---|
| C03 | 02 | X | FRE | @0 Théorie langage @5 02 |
|---|
| C03 | 02 | X | ENG | @0 Language theory @5 02 |
|---|
| C03 | 02 | X | SPA | @0 Teoría lenguaje @5 02 |
|---|
| C03 | 03 | X | FRE | @0 Problème terminaison @5 03 |
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| C03 | 03 | X | ENG | @0 Termination problem @5 03 |
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| C03 | 03 | X | SPA | @0 Problema terminación @5 03 |
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| C03 | 04 | 3 | FRE | @0 Système réécriture @5 04 |
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| C03 | 04 | 3 | ENG | @0 Rewriting systems @5 04 |
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| C03 | 05 | X | FRE | @0 Fonction récursive @5 05 |
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| C03 | 05 | X | ENG | @0 Recursive function @5 05 |
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| C03 | 05 | X | SPA | @0 Función recursiva @5 05 |
|---|
| N21 | | | | @1 285 |
|---|
|
|---|
| pR |
| A30 | 01 | 1 | ENG | @1 Mathematical foundations of computer science. International symposium @2 23 @3 Brno CZE @4 1998-08-24 |
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Le document en format XML
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</keywords><front><div type="abstract" xml:lang="en">In rewriting theory, termination of a rewrite system by Kruskal's theorem implies a theoretical upper bound on the complexity of the system. This bound is, however, far from having been reached by known examples of rewrite systems. All known orderings used to establish termination by Kruskal's theorem yield a multiply recursive bound. Furthermore, the study of the order types of such orderings suggests that the class of multiple recursive functions constitutes the least upper bound. Contradicting this intuition, we construct here a rewrite system which reduces by Kruskal's theorem and whose complexity is not multiply recursive. This system is even totally terminating. This leads to a new lower bound for the complexity of totally terminating rewrite systems and rewrite systems which reduce by Kruskal's theorem. Our construction relies on the Hydra battle using classical tools from ordinal theory and subrecursive functions.</div>
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