Dichotomy theorem for the generalized unique satisfiability problem
Identifieur interne : 00AA10 ( Main/Exploration ); précédent : 00AA09; suivant : 00AA11Dichotomy theorem for the generalized unique satisfiability problem
Auteurs : Laurent Juban [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
Abstract: The unique satisfiability problem, that asks whether there exists a unique solution to a given propositional formula, was extensively studied in the recent years. This paper presents a dichotomy theorem for the unique satisfiability problem, partitioning the instances of the problem between the polynomial-time solvable and coNP-hard cases. We notice that the additional knowledge of a model makes this problem coNP-complete.We compare the polynomial cases of unique satisfiability to the polynomial cases of the usual satisfiability problem and show that they are incomparable. This difference between the polynomial cases is partially due to the necessity to apply parsimonious reductions among the unique satisfiability problems to preserve the number of solutions. In particular, we notice that the unique not-all-equal satisfiability problem, where we ask whether there is a unique model such that each clause has at least one true literal and one false literal, is solvable in polynomial time.
Url:
DOI: 10.1007/3-540-48321-7_27
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 000C86
- to stream Istex, to step Curation: 000C78
- to stream Istex, to step Checkpoint: 002396
- to stream Main, to step Merge: 00B062
- to stream PascalFrancis, to step Corpus: 000A88
- to stream PascalFrancis, to step Curation: 000D82
- to stream PascalFrancis, to step Checkpoint: 000A90
- to stream Main, to step Merge: 00B178
- to stream Main, to step Curation: 00AA10
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Dichotomy theorem for the generalized unique satisfiability problem</title><author><name sortKey="Juban, Laurent" sort="Juban, Laurent" uniqKey="Juban L" first="Laurent" last="Juban">Laurent Juban</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:36A26C2FA4AFB12688D7EC9C12827C7CB7C8AD4B</idno><date when="1999" year="1999">1999</date><idno type="doi">10.1007/3-540-48321-7_27</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-2D3SH7CB-V/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">000C86</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000C86</idno><idno type="wicri:Area/Istex/Curation">000C78</idno><idno type="wicri:Area/Istex/Checkpoint">002396</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">002396</idno><idno type="wicri:doubleKey">0302-9743:1999:Juban L:dichotomy:theorem:for</idno><idno type="wicri:Area/Main/Merge">00B062</idno><idno type="wicri:source">INIST</idno><idno type="RBID">Pascal:99-0527417</idno><idno type="wicri:Area/PascalFrancis/Corpus">000A88</idno><idno type="wicri:Area/PascalFrancis/Curation">000D82</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000A90</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000A90</idno><idno type="wicri:doubleKey">0302-9743:1999:Juban L:dichotomy:theorem:for</idno><idno type="wicri:Area/Main/Merge">00B178</idno><idno type="wicri:Area/Main/Curation">00AA10</idno><idno type="wicri:Area/Main/Exploration">00AA10</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Dichotomy theorem for the generalized unique satisfiability problem</title><author><name sortKey="Juban, Laurent" sort="Juban, Laurent" uniqKey="Juban L" first="Laurent" last="Juban">Laurent Juban</name><affiliation wicri:level="3"><country xml:lang="fr">France</country><wicri:regionArea>LORIA (Universitè Henri Poincarè Nancy 1), BP 239, 54506, Vandœuvre-lèes-Nancy</wicri:regionArea><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lèes-Nancy</settlement></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">France</country></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Comparative study</term><term>Dichotomy</term><term>NP complete problem</term><term>NP hard problem</term><term>Polynomial time</term><term>Problem solving</term><term>Propositional logic</term><term>Satisfiability</term><term>Solution uniqueness</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Dichotomie</term><term>Etude comparative</term><term>Logique propositionnelle</term><term>Problème NP complet</term><term>Problème NP difficile</term><term>Problème satisfiabilité unique</term><term>Résolution problème</term><term>Satisfiabilité</term><term>Temps polynomial</term><term>Unicité solution</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: The unique satisfiability problem, that asks whether there exists a unique solution to a given propositional formula, was extensively studied in the recent years. This paper presents a dichotomy theorem for the unique satisfiability problem, partitioning the instances of the problem between the polynomial-time solvable and coNP-hard cases. We notice that the additional knowledge of a model makes this problem coNP-complete.We compare the polynomial cases of unique satisfiability to the polynomial cases of the usual satisfiability problem and show that they are incomparable. This difference between the polynomial cases is partially due to the necessity to apply parsimonious reductions among the unique satisfiability problems to preserve the number of solutions. In particular, we notice that the unique not-all-equal satisfiability problem, where we ask whether there is a unique model such that each clause has at least one true literal and one false literal, is solvable in polynomial time.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Vandœuvre-lèes-Nancy</li></settlement></list><tree><country name="France"><region name="Grand Est"><name sortKey="Juban, Laurent" sort="Juban, Laurent" uniqKey="Juban L" first="Laurent" last="Juban">Laurent Juban</name></region><name sortKey="Juban, Laurent" sort="Juban, Laurent" uniqKey="Juban L" first="Laurent" last="Juban">Laurent Juban</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 00AA10 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 00AA10 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:36A26C2FA4AFB12688D7EC9C12827C7CB7C8AD4B
|texte= Dichotomy theorem for the generalized unique satisfiability problem
}}
| This area was generated with Dilib version V0.6.33. |  |