Proving Positive Almost-Sure Termination
Identifieur interne : 006B75 ( Hal/Curation ); précédent : 006B74; suivant : 006B76Proving Positive Almost-Sure Termination
Auteurs : Olivier Bournez [France] ; Florent Garnier [France]Source :
Abstract
In order to extend the modeling capabilities of rewriting systems, it is rather natural to consider that the firing of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. We focus here on the problem of termination of a set of probabilistic rewrite rules. A probabilistic rewrite system is said almost surely terminating if the probability that a derivation leads to a normal form is one. Such a system is said positively almost surely terminating if furthermore the mean length of a derivation is finite. We provide several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules. All these techniques subsume classical ones for non-probabilistic systems.
Url:
DOI: 10.1007/b135673
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: Pour aller vers cette notice dans l'étape Curation :006B75
Links to Exploration step
Hal:inria-00000522Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="it">Proving Positive Almost-Sure Termination</title><author><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2360" status="OLD"><idno type="RNSR">199221357D</idno><orgName>Constraints, automatic deduction and software properties proofs</orgName><orgName type="acronym">PROTHEO</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/protheo</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author><author><name sortKey="Garnier, Florent" sort="Garnier, Florent" uniqKey="Garnier F" first="Florent" last="Garnier">Florent Garnier</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2360" status="OLD"><idno type="RNSR">199221357D</idno><orgName>Constraints, automatic deduction and software properties proofs</orgName><orgName type="acronym">PROTHEO</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/protheo</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:inria-00000522</idno><idno type="halId">inria-00000522</idno><idno type="halUri">https://hal.inria.fr/inria-00000522</idno><idno type="url">https://hal.inria.fr/inria-00000522</idno><idno type="doi">10.1007/b135673</idno><date when="2005-04-19">2005-04-19</date><idno type="wicri:Area/Hal/Corpus">006B75</idno><idno type="wicri:Area/Hal/Curation">006B75</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="it">Proving Positive Almost-Sure Termination</title><author><name sortKey="Bournez, Olivier" sort="Bournez, Olivier" uniqKey="Bournez O" first="Olivier" last="Bournez">Olivier Bournez</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2360" status="OLD"><idno type="RNSR">199221357D</idno><orgName>Constraints, automatic deduction and software properties proofs</orgName><orgName type="acronym">PROTHEO</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/protheo</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author><author><name sortKey="Garnier, Florent" sort="Garnier, Florent" uniqKey="Garnier F" first="Florent" last="Garnier">Florent Garnier</name><affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-2360" status="OLD"><idno type="RNSR">199221357D</idno><orgName>Constraints, automatic deduction and software properties proofs</orgName><orgName type="acronym">PROTHEO</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www.inria.fr/equipes/protheo</ref></desc><listRelation><relation active="#struct-160" type="direct"></relation><relation name="UMR7503" active="#struct-441569" type="indirect"></relation><relation active="#struct-300009" type="indirect"></relation><relation active="#struct-300291" type="indirect"></relation><relation active="#struct-300292" type="indirect"></relation><relation active="#struct-300293" type="indirect"></relation><relation active="#struct-2496" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-160" type="direct"><org type="laboratory" xml:id="struct-160" status="OLD"><orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName><orgName type="acronym">LORIA</orgName><desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.loria.fr</ref></desc><listRelation><relation name="UMR7503" active="#struct-441569" type="direct"></relation><relation active="#struct-300009" type="direct"></relation><relation active="#struct-300291" type="direct"></relation><relation active="#struct-300292" type="direct"></relation><relation active="#struct-300293" type="direct"></relation></listRelation></org></tutelle><tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno><idno type="IdRef">02636817X</idno><orgName>Centre National de la Recherche Scientifique</orgName><orgName type="acronym">CNRS</orgName><date type="start">1939-10-19</date><desc><address><country key="FR"></country></address><ref type="url">http://www.cnrs.fr/</ref></desc></org></tutelle><tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName><orgName type="acronym">Inria</orgName><desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic><idno type="DOI">10.1007/b135673</idno></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In order to extend the modeling capabilities of rewriting systems, it is rather natural to consider that the firing of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. We focus here on the problem of termination of a set of probabilistic rewrite rules. A probabilistic rewrite system is said almost surely terminating if the probability that a derivation leads to a normal form is one. Such a system is said positively almost surely terminating if furthermore the mean length of a derivation is finite. We provide several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules. All these techniques subsume classical ones for non-probabilistic systems.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="it">Proving Positive Almost-Sure Termination</title><author role="aut"><persName><forename type="first">Olivier</forename><surname>Bournez</surname></persName><email>Olivier.Bournez@loria.fr</email><idno type="halauthor">63964</idno><affiliation ref="#struct-2360"></affiliation></author><author role="aut"><persName><forename type="first">Florent</forename><surname>Garnier</surname></persName><email>garnier@loria.fr</email><idno type="halauthor">63971</idno><affiliation ref="#struct-2360"></affiliation></author><editor role="depositor"><persName><forename>Olivier</forename><surname>Bournez</surname></persName><email>bournez@lix.polytechnique.fr</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2005-10-26 19:15:07</date><date type="whenModified">2016-05-19 01:09:15</date><date type="whenReleased">2005-10-26 19:15:07</date><date type="whenProduced">2005-04-19</date></edition><respStmt><resp>contributor</resp><name key="103684"><persName><forename>Olivier</forename><surname>Bournez</surname></persName><email>bournez@lix.polytechnique.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00000522</idno><idno type="halUri">https://hal.inria.fr/inria-00000522</idno><idno type="halBibtex">bournez:inria-00000522</idno><idno type="halRefHtml">Jürgen Giesl. 16th International Conference on Rewriting Techniques and Applications - RTA'2005, Apr 2005, Nara/Japan, Springer Verlag, 3467, pp.323-337, 2005, Lecture Notes in Computer Science. <10.1007/b135673></idno><idno type="halRef">Jürgen Giesl. 16th International Conference on Rewriting Techniques and Applications - RTA'2005, Apr 2005, Nara/Japan, Springer Verlag, 3467, pp.323-337, 2005, Lecture Notes in Computer Science. <10.1007/b135673></idno></publicationStmt><seriesStmt><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="LORIA2">Publications du LORIA</idno><idno type="stamp" n="INRIA-NANCY-GRAND-EST">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LORIA-FM" p="LORIA">Méthodes formelles</idno><idno type="stamp" n="LORIA">LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications</idno><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="INRIA-LORRAINE">INRIA Nancy - Grand Est</idno><idno type="stamp" n="LABO-LORIA-SET" p="LORIA">LABO-LORIA-SET</idno></seriesStmt><notesStmt><note type="audience" n="1">Not set</note><note type="invited" n="0">No</note><note type="popular" n="0">No</note><note type="peer" n="1">Yes</note><note type="proceedings" n="1">Yes</note></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="it">Proving Positive Almost-Sure Termination</title><author role="aut"><persName><forename type="first">Olivier</forename><surname>Bournez</surname></persName><email>Olivier.Bournez@loria.fr</email><idno type="halAuthorId">63964</idno><affiliation ref="#struct-2360"></affiliation></author><author role="aut"><persName><forename type="first">Florent</forename><surname>Garnier</surname></persName><email>garnier@loria.fr</email><idno type="halAuthorId">63971</idno><affiliation ref="#struct-2360"></affiliation></author></analytic><monogr><meeting><title>16th International Conference on Rewriting Techniques and Applications - RTA'2005</title><date type="start">2005-04-19</date><settlement>Nara/Japan</settlement></meeting><editor>Jürgen Giesl</editor><imprint><publisher>Springer Verlag</publisher><biblScope unit="serie">Lecture Notes in Computer Science</biblScope><biblScope unit="volume">3467</biblScope><biblScope unit="pp">323-337</biblScope><date type="datePub">2005-04-19</date></imprint></monogr><idno type="doi">10.1007/b135673</idno></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><classCode scheme="halTypology" n="COMM">Conference papers</classCode></textClass><abstract xml:lang="en">In order to extend the modeling capabilities of rewriting systems, it is rather natural to consider that the firing of rules can be subject to some probabilistic laws. Considering rewrite rules subject to probabilities leads to numerous questions about the underlying notions and results. We focus here on the problem of termination of a set of probabilistic rewrite rules. A probabilistic rewrite system is said almost surely terminating if the probability that a derivation leads to a normal form is one. Such a system is said positively almost surely terminating if furthermore the mean length of a derivation is finite. We provide several results and techniques in order to prove positive almost sure termination of a given set of probabilistic rewrite rules. All these techniques subsume classical ones for non-probabilistic systems.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Hal/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 006B75 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Curation/biblio.hfd -nk 006B75 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Hal
|étape= Curation
|type= RBID
|clé= Hal:inria-00000522
|texte= Proving Positive Almost-Sure Termination
}}
| This area was generated with Dilib version V0.6.33. |  |