Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions
Identifieur interne : 000B82 ( Hal/Curation ); précédent : 000B81; suivant : 000B83Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions
Auteurs : Olivier Bournez [France] ; Walid Gomaa [Égypte] ; Emmanuel Hainry [France]Source :
- International Journal of Unconventional Computing [ 1548-7199 ] ; 2011.
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Abstract
Recursive analysis is the most classical approach to model and discuss computations over the real numbers.Recently, it has been shown that computability classes of functions in the sense of recursive analysis can be defined (or characterized) in an algebraic machine independent way, without resorting to Turing machines. In particular nice connections between the class of computable functions (and some of its sub- and sup-classes) over the reals and algebraically defined (sub- and sup-) classes of R-recursive functions à la Moore 96 have been obtained. However, until now, this has been done only at the computability level, and not at the complexity level. In this paper we provide a framework that allows us to dive into the complexity level of real functions. In particular we provide the first algebraic characterization of polynomial-time computable functions over the reals. This framework opens the field of implicit complexity of analog functions, and also provides a new reading of some of the existing characterizations at the computability level.
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In particular nice connections between the class of computable functions (and some of its sub- and sup-classes) over the reals and algebraically defined (sub- and sup-) classes of R-recursive functions à la Moore 96 have been obtained. However, until now, this has been done only at the computability level, and not at the complexity level. In this paper we provide a framework that allows us to dive into the complexity level of real functions. In particular we provide the first algebraic characterization of polynomial-time computable functions over the reals. This framework opens the field of implicit complexity of analog functions, and also provides a new reading of some of the existing characterizations at the computability level.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions</title><author role="aut"><persName><forename type="first">Olivier</forename><surname>Bournez</surname></persName><email>Olivier.Bournez@lix.polytechnique.fr</email><idno type="halauthor">447097</idno><orgName ref="#struct-300340"></orgName><affiliation ref="#struct-2071"></affiliation></author><author role="aut"><persName><forename type="first">Walid</forename><surname>Gomaa</surname></persName><email>walid.gomaa@ejust.edu.eg</email><idno type="halauthor">662274</idno><orgName ref="#struct-301668"></orgName><affiliation ref="#struct-102330"></affiliation></author><author role="aut"><persName><forename type="first">Emmanuel</forename><surname>Hainry</surname></persName><email>Emmanuel.Hainry@loria.fr</email><idno type="idhal">emmanuel-hainry</idno><idno type="halauthor">530263</idno><orgName ref="#struct-300291"></orgName><affiliation ref="#struct-29797"></affiliation></author><editor role="depositor"><persName><forename>Emmanuel</forename><surname>Hainry</surname></persName><email>Emmanuel.Hainry@ens-lyon.org</email></editor></titleStmt><editionStmt><edition n="v1" type="current"><date type="whenSubmitted">2011-11-24 11:51:55</date><date type="whenWritten">2011-04</date><date type="whenModified">2015-09-22 01:12:48</date><date type="whenReleased">2011-11-24 13:18:07</date><date type="whenProduced">2011</date><date type="whenEndEmbargoed">2011-11-24</date><ref type="file" target="https://hal.inria.fr/hal-00644361/document"><date notBefore="2011-11-24"></date></ref><ref type="file" subtype="author" n="1" target="https://hal.inria.fr/hal-00644361/file/ijuc_h.pdf"><date notBefore="2011-11-24"></date></ref></edition><respStmt><resp>contributor</resp><name key="117979"><persName><forename>Emmanuel</forename><surname>Hainry</surname></persName><email>Emmanuel.Hainry@ens-lyon.org</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">hal-00644361</idno><idno type="halUri">https://hal.inria.fr/hal-00644361</idno><idno type="halBibtex">bournez:hal-00644361</idno><idno type="halRefHtml">International Journal of Unconventional Computing, Old City Publishing, 2011, 7 (5), pp.331-351</idno><idno type="halRef">International Journal of Unconventional Computing, Old City Publishing, 2011, 7 (5), pp.331-351</idno></publicationStmt><seriesStmt><idno type="stamp" n="CNRS">CNRS - 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Institut National de Recherche en Informatique et en Automatique</idno></seriesStmt><notesStmt><note type="commentary">Accepted for publication in International Journal of Unconventional Computing</note><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">Algebraic Characterizations of Complexity-Theoretic Classes of Real Functions</title><author role="aut"><persName><forename type="first">Olivier</forename><surname>Bournez</surname></persName><email>Olivier.Bournez@lix.polytechnique.fr</email><idno type="halAuthorId">447097</idno><orgName ref="#struct-300340"></orgName><affiliation ref="#struct-2071"></affiliation></author><author role="aut"><persName><forename type="first">Walid</forename><surname>Gomaa</surname></persName><email>walid.gomaa@ejust.edu.eg</email><idno type="halAuthorId">662274</idno><orgName ref="#struct-301668"></orgName><affiliation ref="#struct-102330"></affiliation></author><author role="aut"><persName><forename type="first">Emmanuel</forename><surname>Hainry</surname></persName><email>Emmanuel.Hainry@loria.fr</email><idno type="idHal">emmanuel-hainry</idno><idno type="halAuthorId">530263</idno><orgName ref="#struct-300291"></orgName><affiliation ref="#struct-29797"></affiliation></author></analytic><monogr><idno type="halJournalId" status="VALID">39452</idno><idno type="issn">1548-7199</idno><idno type="eissn">1548-7202</idno><title level="j">International Journal of Unconventional Computing</title><imprint><publisher>Old City Publishing</publisher><biblScope unit="volume">7</biblScope><biblScope unit="issue">5</biblScope><biblScope unit="pp">331-351</biblScope><date type="datePub">2011</date></imprint></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="en">English</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">Recursive Analysis</term><term xml:lang="en">Polynomial Time</term><term xml:lang="en">Algebraic Characterization</term><term xml:lang="en">Real Computation</term><term xml:lang="en">Oracle Turing Machines</term></keywords><classCode scheme="halDomain" n="info.info-cc">Computer Science [cs]/Computational Complexity [cs.CC]</classCode><classCode scheme="halTypology" n="ART">Journal articles</classCode></textClass><abstract xml:lang="en">Recursive analysis is the most classical approach to model and discuss computations over the real numbers.Recently, it has been shown that computability classes of functions in the sense of recursive analysis can be defined (or characterized) in an algebraic machine independent way, without resorting to Turing machines. In particular nice connections between the class of computable functions (and some of its sub- and sup-classes) over the reals and algebraically defined (sub- and sup-) classes of R-recursive functions à la Moore 96 have been obtained. However, until now, this has been done only at the computability level, and not at the complexity level. In this paper we provide a framework that allows us to dive into the complexity level of real functions. In particular we provide the first algebraic characterization of polynomial-time computable functions over the reals. This framework opens the field of implicit complexity of analog functions, and also provides a new reading of some of the existing characterizations at the computability level.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
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