Definability and Compression

Afrati, F; Leiss, H; De Rougemont, M

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	https://dspace.lib.ntua.gr/xmlui/handle/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