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Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
- solutions by mathematical methods of problems emerging in computer science
- solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, & algebraic and categorical methods.
Authors: Séébold, Patrice
Article Type: Research Article
Abstract: We study length-k-overlap-free binary infinite words, i.e., binary infinite words which can contain only overlaps xyxyx with |x| ≤ k − 1. We prove that no such word can be generated by a morphism, except if k = 1. On the other hand, for every k ≥ 2, there exist length-k-overlap-free binary infinite words which are not length-(k − 1)-overlap-free. As an application, we prove that, for every non-negative integer n, there exist infinitely many length-k-overlap-free binary infinite partial words with n holes.
Keywords: Repetition-freeness, length-k-overlaps, partial words, Thue-Morse word, infinite words
Citation: Fundamenta Informaticae, vol. 116, no. 1-4, pp. 251-263, 2012
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