<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-02143807</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-14T17:08:54+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">The operator approach to entropy games</title>
            <author role="aut">
              <persName>
                <forename type="first">Marianne</forename>
                <surname>Akian</surname>
              </persName>
              <email type="md5">ca9847495e168bb0a4582a6d8e657df9</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">marianne-akian</idno>
              <idno type="idhal" notation="numeric">830429</idno>
              <idno type="halauthorid" notation="string">111173-830429</idno>
              <idno type="ARXIV">https://arxiv.org/a/akian_m_1</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8569-7622</idno>
              <affiliation ref="#struct-450091"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Stéphane</forename>
                <surname>Gaubert</surname>
              </persName>
              <email type="md5">968c5e40f47dae596f29786f18220395</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="string">stephane-gaubert</idno>
              <idno type="idhal" notation="numeric">1887</idno>
              <idno type="halauthorid" notation="string">577-1887</idno>
              <idno type="IDREF">https://www.idref.fr/104895306</idno>
              <affiliation ref="#struct-450091"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Julien</forename>
                <surname>Grand-Clément</surname>
              </persName>
              <email type="md5">4604e40f15353715b5f1c7b379a5ccd1</email>
              <email type="domain">columbia.edu</email>
              <idno type="idhal" notation="numeric">1048076</idno>
              <idno type="halauthorid" notation="string">1292840-1048076</idno>
              <orgName ref="#struct-75524"/>
              <affiliation ref="#struct-75524"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jérémie</forename>
                <surname>Guillaud</surname>
              </persName>
              <email type="md5">d21ed03b3ecb4537fe99485a7bd7fb9a</email>
              <email type="domain">inria.fr</email>
              <idno type="idhal" notation="numeric">1024190</idno>
              <idno type="halauthorid" notation="string">1272888-1024190</idno>
              <orgName ref="#struct-300340"/>
              <affiliation ref="#struct-542174"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Marianne</forename>
                <surname>Akian</surname>
              </persName>
              <email type="md5">ca9847495e168bb0a4582a6d8e657df9</email>
              <email type="domain">inria.fr</email>
            </editor>
            <funder ref="#projanr-36822"/>
            <funder>The authors were partially supported by the ANR through the MALTHY INS project, and by the Gaspard Monge corporate sponsorship Program (PGMO) of EDF, Orange, Thales and Fondation Mathématique Jacques Hadmard.</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2019-05-29 15:53:43</date>
              <date type="whenModified">2025-10-27 09:36:02</date>
              <date type="whenReleased">2019-05-29 15:53:43</date>
              <date type="whenProduced">2019</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/1904.05151"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102216">
                <persName>
                  <forename>Marianne</forename>
                  <surname>Akian</surname>
                </persName>
                <email type="md5">ca9847495e168bb0a4582a6d8e657df9</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-02143807</idno>
            <idno type="halUri">https://hal.science/hal-02143807</idno>
            <idno type="halBibtex">akian:hal-02143807</idno>
            <idno type="halRefHtml">&lt;i&gt;Theory of Computing Systems&lt;/i&gt;, 2019, 63, pp.1089-1130. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s00224-019-09925-z"&gt;&amp;#x27E8;10.1007/s00224-019-09925-z&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Theory of Computing Systems, 2019, 63, pp.1089-1130. &amp;#x27E8;10.1007/s00224-019-09925-z&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="ENSMP" corresp="PARISTECH">MINES ParisTech</idno>
            <idno type="stamp" n="ENS-PARIS">Ecole Normale Supérieure de Paris</idno>
            <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="INRIA-ROCQ">INRIA Paris - Rocquencourt</idno>
            <idno type="stamp" n="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="PSL">Université Paris sciences et lettres</idno>
            <idno type="stamp" n="UNIV-PARIS-SACLAY">Université Paris-Saclay</idno>
            <idno type="stamp" n="INRIA-SACLAY-2015" corresp="UNIV-PARIS-SACLAY">INRIA-SACLAY-2015</idno>
            <idno type="stamp" n="X-SACLAY" corresp="UNIV-PARIS-SACLAY">X-SACLAY</idno>
            <idno type="stamp" n="INRIA-PSL">INRIA-PSL</idno>
            <idno type="stamp" n="SORBONNE-UNIVERSITE">Sorbonne Université</idno>
            <idno type="stamp" n="SORBONNE-UNIV" corresp="SORBONNE-UNIVERSITE">Sorbonne Université 01/01/2018</idno>
            <idno type="stamp" n="SU-SCIENCES" corresp="SORBONNE-UNIVERSITE">Faculté des Sciences de Sorbonne Université</idno>
            <idno type="stamp" n="SU-SCI" corresp="SORBONNE-UNIVERSITE">Sciences - Sorbonne Université</idno>
            <idno type="stamp" n="LPENS" corresp="ENS-PARIS">Laboratoire de physique de l'ENS</idno>
            <idno type="stamp" n="UP-SCIENCES">Université Paris Cité - Faculté des Sciences</idno>
            <idno type="stamp" n="ENSMP-PSL" corresp="PSL">MINES ParisTech - École nationale supérieure des mines de Paris - PSL</idno>
            <idno type="stamp" n="ENS-PSL" corresp="PSL">École normale supérieure - PSL</idno>
            <idno type="stamp" n="SU-TI">Sorbonne Université - Texte Intégral</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="ALLIANCE-SU"> Alliance Sorbonne Université</idno>
            <idno type="stamp" n="INRIAARTDOI">INRIAARTDOI</idno>
            <idno type="stamp" n="INRIA-ETATSUNIS">Copublications Inria-Etats-Unis</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">The operator approach to entropy games</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Marianne</forename>
                    <surname>Akian</surname>
                  </persName>
                  <email type="md5">ca9847495e168bb0a4582a6d8e657df9</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">marianne-akian</idno>
                  <idno type="idhal" notation="numeric">830429</idno>
                  <idno type="halauthorid" notation="string">111173-830429</idno>
                  <idno type="ARXIV">https://arxiv.org/a/akian_m_1</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8569-7622</idno>
                  <affiliation ref="#struct-450091"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Stéphane</forename>
                    <surname>Gaubert</surname>
                  </persName>
                  <email type="md5">968c5e40f47dae596f29786f18220395</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="string">stephane-gaubert</idno>
                  <idno type="idhal" notation="numeric">1887</idno>
                  <idno type="halauthorid" notation="string">577-1887</idno>
                  <idno type="IDREF">https://www.idref.fr/104895306</idno>
                  <affiliation ref="#struct-450091"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Julien</forename>
                    <surname>Grand-Clément</surname>
                  </persName>
                  <email type="md5">4604e40f15353715b5f1c7b379a5ccd1</email>
                  <email type="domain">columbia.edu</email>
                  <idno type="idhal" notation="numeric">1048076</idno>
                  <idno type="halauthorid" notation="string">1292840-1048076</idno>
                  <orgName ref="#struct-75524"/>
                  <affiliation ref="#struct-75524"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jérémie</forename>
                    <surname>Guillaud</surname>
                  </persName>
                  <email type="md5">d21ed03b3ecb4537fe99485a7bd7fb9a</email>
                  <email type="domain">inria.fr</email>
                  <idno type="idhal" notation="numeric">1024190</idno>
                  <idno type="halauthorid" notation="string">1272888-1024190</idno>
                  <orgName ref="#struct-300340"/>
                  <affiliation ref="#struct-542174"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">19610</idno>
                <idno type="issn">1432-4350</idno>
                <idno type="eissn">1433-0490</idno>
                <title level="j">Theory of Computing Systems</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">63</biblScope>
                  <biblScope unit="pp">1089-1130</biblScope>
                  <date type="datePub">2019</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1904.05151</idno>
              <idno type="doi">10.1007/s00224-019-09925-z</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Stochastic games</term>
                <term xml:lang="en">Risk sensitive control</term>
                <term xml:lang="en">Perron eigenvalues</term>
                <term xml:lang="en">Policy iteration</term>
                <term xml:lang="en">Shapley operators</term>
              </keywords>
              <classCode scheme="classification">1991 Mathematics Subject Classification. G.2.1 Combinatorial algorithms, F.2.1 Numerical Algorithms and Problems</classCode>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Entropy games and matrix multiplication games have been recently introduced by Asarin et al. They model the situation in which one player (Despot) wishes to minimize the growth rate of a matrix product, whereas the other player (Tribune) wishes to maximize it. We develop an operator approach to entropy games. This allows us to show that entropy games can be cast as stochastic mean payoff games in which some action spaces are simplices and payments are given by a relative entropy (Kullback-Leibler divergence). In this way, we show that entropy games with a fixed number of states belonging to Despot can be solved in polynomial time. This approach also allows us to solve these games by a policy iteration algorithm, which we compare with the spectral simplex algorithm developed by Protasov.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-450091" status="VALID">
          <idno type="RNSR">201621988K</idno>
          <idno type="ROR">https://ror.org/04fvec703</idno>
          <orgName>Méthodes tropicales: structures, algorithmes et interactions</orgName>
          <orgName type="acronym">TROPICAL</orgName>
          <date type="start">2016-01-01</date>
          <date type="end">2026-12-31</date>
          <desc>
            <address>
              <addrLine>1 Rue Honoré d'Estienne d'Orves91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/tropical</ref>
          </desc>
          <listRelation>
            <relation active="#struct-89626" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-300340" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1225635" type="direct"/>
            <relation active="#struct-118511" type="indirect"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-75524" status="VALID">
          <idno type="ROR">https://ror.org/0190ak572</idno>
          <orgName>Columbia University [New York]</orgName>
          <desc>
            <address>
              <addrLine>Columbia University in the City of New York, 2960 Broadway, New York, NY 10027-6902</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">https://www.columbia.edu/</ref>
          </desc>
        </org>
        <org type="researchteam" xml:id="struct-542174" status="VALID">
          <idno type="RNSR">201321103L</idno>
          <idno type="ROR">https://ror.org/04e2h0037</idno>
          <orgName>QUANTum Information Circuits</orgName>
          <orgName type="acronym">QUANTIC</orgName>
          <date type="start">2018-01-01</date>
          <date type="end">2026-12-31</date>
          <desc>
            <address>
              <addrLine>45, rue d'Ulm 75230 Paris Cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/quantic</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301492" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
            <relation active="#struct-413221" type="direct"/>
            <relation active="#struct-1004921" type="direct"/>
            <relation name="UMR8023" active="#struct-441569" type="indirect"/>
            <relation active="#struct-557826" type="indirect"/>
            <relation active="#struct-1136774" type="indirect"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-1175218" type="direct"/>
            <relation active="#struct-454310" type="indirect"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <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"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</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"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-1225635" status="VALID">
          <idno type="ROR">https://ror.org/026839t73</idno>
          <orgName>Centre Inria de l'Institut Polytechnique de Paris</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'Orves –Bâtiment Alan Turing –Campus de l'École Polytechnique –91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-118511" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301492" status="VALID">
          <idno type="IdRef">026375249</idno>
          <idno type="ROR">https://ror.org/04y8cs423</idno>
          <orgName>Mines Paris - PSL (École nationale supérieure des mines de Paris)</orgName>
          <date type="start">1783-01-01</date>
          <desc>
            <address>
              <addrLine>60, boulevard Saint-Michel 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.minesparis.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-564132" status="VALID">
          <idno type="IdRef">241597595</idno>
          <idno type="ISNI">0000 0004 1784 3645</idno>
          <idno type="ROR">https://ror.org/013cjyk83</idno>
          <orgName>Université Paris Sciences et Lettres</orgName>
          <orgName type="acronym">PSL</orgName>
          <desc>
            <address>
              <addrLine>60 rue Mazarine 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.psl.eu/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-413221" status="VALID">
          <idno type="IdRef">221333754</idno>
          <idno type="ROR">https://ror.org/02en5vm52</idno>
          <orgName>Sorbonne Université</orgName>
          <orgName type="acronym">SU</orgName>
          <date type="start">2018-01-01</date>
          <desc>
            <address>
              <addrLine>21 rue de l’École de médecine - 75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.sorbonne-universite.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-1004921" status="VALID">
          <idno type="IdRef">192153935</idno>
          <idno type="RNSR">201922973T</idno>
          <idno type="ROR">https://ror.org/03a26mh11</idno>
          <orgName>Laboratoire de physique de l'ENS - ENS Paris</orgName>
          <orgName type="acronym">LPENS</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>24, rue Lhomond75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.lpens.ens.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413221" type="direct"/>
            <relation name="UMR8023" active="#struct-441569" type="direct"/>
            <relation active="#struct-557826" type="direct"/>
            <relation active="#struct-1136774" type="direct"/>
            <relation active="#struct-59704" type="indirect"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-557826" status="VALID">
          <idno type="IdRef">236453505</idno>
          <idno type="ISNI">0000 0004 7885 7602</idno>
          <idno type="ROR">https://ror.org/05f82e368</idno>
          <orgName>Université Paris Cité</orgName>
          <orgName type="acronym">UPCité</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <addrLine>85 boulevard Saint-Germain75006 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-paris.fr/</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-1136774" status="VALID">
          <orgName>Département de Physique de l'ENS-PSL</orgName>
          <desc>
            <address>
              <addrLine>24 rue Lhomond, 75005 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.phys.ens.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-59704" type="direct"/>
            <relation active="#struct-564132" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-59704" status="VALID">
          <idno type="IdRef">031738419</idno>
          <idno type="ISNI">0000000123532622</idno>
          <idno type="ROR">https://ror.org/05a0dhs15</idno>
          <orgName>École normale supérieure - Paris</orgName>
          <orgName type="acronym">ENS-PSL</orgName>
          <date type="start">1985-07-24</date>
          <desc>
            <address>
              <addrLine>45, Rue d'Ulm - 75230 Paris cedex 05</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens.psl.eu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-564132" type="direct"/>
          </listRelation>
        </org>
        <org type="department" xml:id="struct-1175218" status="VALID">
          <idno type="ROR">https://ror.org/03cjm2544</idno>
          <orgName>Centre Inria de Sorbonne Université</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-454310" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-454310" status="VALID">
          <idno type="IdRef">241614864</idno>
          <idno type="RNSR">196718247G</idno>
          <idno type="ROR">https://ror.org/05eyd5d35</idno>
          <orgName>Centre Inria de Paris</orgName>
          <date type="start">2016-03-10</date>
          <desc>
            <address>
              <addrLine>48 Rue Barrault, 75013 Paris</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/paris</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-36822" status="VALID">
          <idno type="anr">ANR-13-INSE-0003</idno>
          <idno type="program">Ingénierie Numérique et Sécurité</idno>
          <orgName>MALTHY</orgName>
          <desc>Méthodes ALgèbriques pour la vérification de modèles Temporisés et HYbrides</desc>
          <date type="start">2013</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>