A Theoretical Limit for Safety Verification Techniques with Regular Fix-point Computations
Identifieur interne : 003720 ( Hal/Checkpoint ); précédent : 003719; suivant : 003721A Theoretical Limit for Safety Verification Techniques with Regular Fix-point Computations
Auteurs : Yohan Boichut [France] ; Pierre-Cyrille Heam [France]Source :
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Abstract
In computer aided verification, the reachability problem is particularly relevant for safety analyses. Given a regular tree language L, a term t and a relation R, the reachability problem consists in deciding whether a sequence of terms, beginning with a term of L and terminating on t and such that two successive terms of this sequence are in relation according to R, is constructable. In this case, the term t is said to be reachable, otherwise it is said unreachable. This problem is decidable for particular kinds of relations, but it is known to be undecidable in general, even if L is finite. Several approaches to tackle the unreachability problem are based on the computation of an R-closed regular language containing L. In this paper we show a theoretical limit to this kind of approaches for this problem.
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Given a regular tree language L, a term t and a relation R, the reachability problem consists in deciding whether a sequence of terms, beginning with a term of L and terminating on t and such that two successive terms of this sequence are in relation according to R, is constructable. In this case, the term t is said to be reachable, otherwise it is said unreachable. This problem is decidable for particular kinds of relations, but it is known to be undecidable in general, even if L is finite. Several approaches to tackle the unreachability problem are based on the computation of an R-closed regular language containing L. In this paper we show a theoretical limit to this kind of approaches for this problem.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">A Theoretical Limit for Safety Verification Techniques with Regular Fix-point Computations</title><author role="aut"><persName><forename type="first">Yohan</forename><surname>Boichut</surname></persName><email></email><idno type="halauthor">61788</idno><affiliation ref="#struct-54175"></affiliation></author><author role="aut"><persName><forename type="first">Pierre-Cyrille</forename><surname>Heam</surname></persName><email></email><idno type="idhal">pierre-cyrille-heam</idno><idno type="halauthor">241566</idno><affiliation ref="#struct-866"></affiliation></author><editor role="depositor"><persName><forename>Rapport De Recherche</forename><surname>Inria</surname></persName><email>rrrt-editeurs@inria.fr</email></editor></titleStmt><editionStmt><edition n="v1"><date type="whenSubmitted">2008-01-15 09:27:55</date></edition><edition n="v2" type="current"><date type="whenSubmitted">2008-01-15 12:57:13</date><date type="whenModified">2016-05-19 01:12:05</date><date type="whenReleased">2008-01-15 12:57:42</date><date type="whenProduced">2008</date><date type="whenEndEmbargoed">2008-01-15</date><ref type="file" target="https://hal.inria.fr/inria-00204579v2/document"><date notBefore="2008-01-15"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.inria.fr/inria-00204579/file/RR-6411.pdf"><date notBefore="2008-01-15"></date></ref></edition><respStmt><resp>contributor</resp><name key="111068"><persName><forename>Rapport De Recherche</forename><surname>Inria</surname></persName><email>rrrt-editeurs@inria.fr</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">inria-00204579</idno><idno type="halUri">https://hal.inria.fr/inria-00204579</idno><idno type="halBibtex">boichut:inria-00204579</idno><idno type="halRefHtml">[Research Report] RR-6411, INRIA. 2008, pp.6</idno><idno type="halRef">[Research Report] RR-6411, INRIA. 2008, pp.6</idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno><idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno><idno type="stamp" n="UNIV-FCOMTE">Université de Franche-Comté</idno><idno type="stamp" n="INPL">Institut National Polytechnique de Lorraine</idno><idno type="stamp" n="INRIA-RRRT">Rapports de recherche et Technique de l'Inria</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="INRIA2">INRIA 2</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><idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno><idno type="stamp" n="UNIV-BM">Université de Technologie de Belfort-Montbeliard</idno><idno type="stamp" n="ENSMM">Ecole Nationale Supérieure de Mécanique et des Microtechniques</idno><idno type="stamp" n="FEMTO-ST" p="UNIV-FCOMTE">Franche-Comté Electronique, Mécanique, Thermique et Optique - 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Given a regular tree language L, a term t and a relation R, the reachability problem consists in deciding whether a sequence of terms, beginning with a term of L and terminating on t and such that two successive terms of this sequence are in relation according to R, is constructable. In this case, the term t is said to be reachable, otherwise it is said unreachable. This problem is decidable for particular kinds of relations, but it is known to be undecidable in general, even if L is finite. Several approaches to tackle the unreachability problem are based on the computation of an R-closed regular language containing L. In this paper we show a theoretical limit to this kind of approaches for this problem.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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