Definability and Compression

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dc.contributor.author Afrati, F en
dc.contributor.author Leiss, H en
dc.contributor.author De Rougemont, M en
dc.date.accessioned 2014-03-01T01:18:48Z
dc.date.available 2014-03-01T01:18:48Z
dc.date.issued 2003 en
dc.identifier.issn 0169-2968 en
dc.identifier.uri http://hdl.handle.net/123456789/15213
dc.relation.uri http://www.scopus.com/inward/record.url?eid=2-s2.0-0141830866&partnerID=40&md5=5dcb0e758b2afbaf848fa1c14968f986 en
dc.relation.uri http://iospress.metapress.com/openurl.asp?genre=article&issn=0169-2968&volume=56&issue=1&spage=155 en
dc.relation.uri http://www.informatik.uni-trier.de/~ley/db/journals/fuin/fuin56.html#AfratiLR03 en
dc.subject Definability en
dc.subject Lempel-Ziv-78 en
dc.subject Logic en
dc.subject String compression en
dc.subject.classification Computer Science, Software Engineering en
dc.subject.classification Mathematics, Applied en
dc.subject.other Algorithms en
dc.subject.other Computational complexity en
dc.subject.other Formal logic en
dc.subject.other Graph theory en
dc.subject.other Problem solving en
dc.subject.other String compression en
dc.subject.other Data compression en
dc.title Definability and Compression en
heal.type journalArticle en
heal.language English en
heal.publicationDate 2003 en
heal.abstract A compression algorithm takes a finite structure of a class K as input and produces a finite structure of a different class K' as output. Given a property P on the class K defined in a logic ℒ, we study the definability of property P on the class K'. We consider two compression schemes on unary ordered structures (strings), compression by run-length encoding and the classical Lempel-Ziv-78 scheme. First-order properties of strings are first-order on run-length compressed strings, but this fails for images, i.e. 2-dimensional strings. We present simple first-order properties of strings which are not first-order definable on strings compressed with the Lempel-Ziv-78 compression scheme. We show that all properties of strings that are first-order definable on strings are definable on Lempel-Ziv compressed strings in FO(TC), the extension of first-order logic with the transitive closure operator. We define a subclass ℱ of the first-order properties of strings such that if P is a property in ℱ, it is also first-order definable on the Lempel-Ziv compressed strings. Monadic second-order properties of strings, i.e. regular languages, are dyadic second-order definable on Lempel-Ziv compressed strings. en
heal.publisher IOS PRESS en
heal.journalName Fundamenta Informaticae en
dc.identifier.isi ISI:000186087600010 en
dc.identifier.volume 56 en
dc.identifier.issue 1-2 en
dc.identifier.spage 155 en
dc.identifier.epage 180 en

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