Detecting leftmost maximal periodicities
Discrete Applied Mathematics - Combinatorics and complexity
Handbook of formal languages, vol. 1
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Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
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Journal of the ACM (JACM)
Mathematical Theory of L Systems
Mathematical Theory of L Systems
Automata: Theoretic Aspects of Formal Power Series
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Complexité des Facteurs des Mots Infinis Engendrés par Morphimes Itérés
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Bornes inferieures sur la complexite des facteurs des mots infinis engendres par morphimes iteres
STACS '84 Proceedings of the Symposium of Theoretical Aspects of Computer Science
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FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
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FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Application of Lempel--Ziv factorization to the approximation of grammar-based compression
Theoretical Computer Science
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Estimating the Entropy Rate of Spike Trains via Lempel-Ziv Complexity
Neural Computation
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The Lempel–Ziv complexity is a fundamental measure of complexity for words, closely connected with the famous LZ77, LZ78 compression algorithms. We investigate this complexity measure for one of the most important families of infinite words in combinatorics, namely the fixed points of morphisms. We give a complete characterisation of the complexity classes which are Θ(1), Θ(logn), and Θ(n$^{\rm 1/{\it k}}$), k∈ℕ, k ≥2, depending on the periodicity of the word and the growth function of the morphism. The relation with the well-known classification of Ehrenfeucht, Lee, Rozenberg, and Pansiot for factor complexity classes is also investigated. The two measures complete each other, giving an improved picture for the complexity of these infinite words.