Succinct representations of graphs
Information and Control
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Text compression
Elements of information theory
Elements of information theory
P-complete problems in data compression
Theoretical Computer Science
String matching in Lempel-Ziv compressed strings
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Elementary Computability, Formal Languages and Automata
Elementary Computability, Formal Languages and Automata
Probabilistic Abstraction for Model Checking: An Approach Based on Property Testing
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Efficient Algorithms for Lempel-Zip Encoding (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Complexity of Problems on Graphs Represented as OBDDs (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
A Text Compression Scheme That Allows Fast Searching Directly in the Compressed File
CPM '94 Proceedings of the 5th Annual Symposium on Combinatorial Pattern Matching
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
A Unifying Framework for Compressed Pattern Matching
SPIRE '99 Proceedings of the String Processing and Information Retrieval Symposium & International Workshop on Groupware
Regular expression searching on compressed text
Journal of Discrete Algorithms
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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.