Elements of information theory
Elements of information theory
Approximation algorithms for grammar-based compression
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Offline Dictionary-Based Compression
DCC '99 Proceedings of the Conference on Data Compression
A Unifying Framework for Compressed Pattern Matching
SPIRE '99 Proceedings of the String Processing and Information Retrieval Symposium & International Workshop on Groupware
Some Theory and Practice of Greedy Off-Line Textual Substitution
DCC '98 Proceedings of the Conference on Data Compression
Data compression: methods and complexity issues.
Data compression: methods and complexity issues.
Unsupervised language acquisition
Unsupervised language acquisition
Grammar-based codes: a new class of universal lossless source codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Universal lossless compression via multilevel pattern matching
IEEE Transactions on Information Theory
Application of Lempel--Ziv factorization to the approximation of grammar-based compression
Theoretical Computer Science
Proceedings of the 2006 ACM SIGPLAN symposium on Partial evaluation and semantics-based program manipulation
Optimization issues in inverted index-based entity annotation
Proceedings of the 3rd international conference on Scalable information systems
Nonlinear dimensionality reduction by locally linear inlaying
IEEE Transactions on Neural Networks
A fully linear-time approximation algorithm for grammar-based compression
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
Theoretical Computer Science
Pattern matching in lempel-Ziv compressed strings: fast, simple, and deterministic
ESA'11 Proceedings of the 19th European conference on Algorithms
One-dimensional staged self-assembly
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Efficient memory representation of XML documents
DBPL'05 Proceedings of the 10th international conference on Database Programming Languages
An efficient pattern matching algorithm on a subclass of context free grammars
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Improving time and space complexity for compressed pattern matching
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Improved grammar-based compressed indexes
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
One-dimensional staged self-assembly
Natural Computing: an international journal
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We consider the problem of finding the smallest context-free grammar that generates exactly one given string of length n. The size of this grammar is of theoretical interest as an efficiently computable variant of Kolmogorov complexity. The problem is of practical importance in areas such as data compression and pattern extraction.The smallest grammar is known to be hard to approximate to within a constant factor, and an o(logn/log logn) approximation would require progress on a long-standing algebraic problem [10]. Previously, the best proved approximation ratio was O(n1/2) for the Bisection algorithm [8]. Our main result is an exponential improvement of this ratio; we give an O(log (n/g*)) approximation algorithm, where g* is the size of the smallest grammar.We then consider other computable variants of Kolomogorov complexity. In particular we give an O(log2 n) approximation for the smallest non-deterministic finite automaton with advice that produces a given string. We also apply our techniques to "advice-grammars" and "edit-grammars", two other natural models of string complexity.