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Logic in Computer Science, Symposium on (2000)
Santa Barbara, California
June 26, 2000 to June 29, 2000
ISSN: 1043-6871
ISBN: 0-7695-0725-5
pp: 63
Foto Afrati , National Technical University Athens
Hans Leiß , Universit?t M?nchen
Michel de Rougemont , Universit? Paris-II and LRI B?timent
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 {cal L}, we study the definability of property P on the class K'. We consider two compression schemas on unary ordered structures (words), compression by run-length encoding and the classical Lempel-Ziv.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 compression schema.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 cal F of the first-order properties of strings such that if L is defined by a property in cal F, it is also first-order definable on the Lempel-Ziv compressed strings. Monadic second-order properties of strings are dyadic second order definable on Lempel-Ziv compressed strings.
logic, compression, Lempel-Ziv

F. Afrati, M. de Rougemont and H. Leiß, "Definability and Compression," Logic in Computer Science, Symposium on(LICS), Santa Barbara, California, 2000, pp. 63.
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