Repetition of subwords in DOL languages
Information and Control
Properties of words and recognizability of fixed points of a substitution
Theoretical Computer Science
An algorithm to symbolically describe flows on surfaces
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Substitutions and interval exchange transformations of rotation class
Theoretical Computer Science
Handbook of Formal Languages
Mathematical Theory of L Systems
Mathematical Theory of L Systems
Repetitiveness of D0L-Languages Is Decidable in Polynomial Time
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Generalized Sturmian Languages
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
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We introduce, extend and apply some relationships between formal language theory and surface theory. First we show how boundaries of languages topologized with the Cantor metric can be mapped to sets of curves on surfaces, namely laminations. Second we present how and when endomorphisms of free monoids, i.e. substitutions, can be mapped to automorphisms of surfaces, so that D0L-systems correspond to iterations of these automorphisms. Third, we apply these ideas to construct sets of non-periodic irreducible automorphisms of surfaces following [14,35,43], so that the involved proofs do not use any differential or algebraic tools, but, accordingly, substitution and D0L-system theory of [11,12,31,32,37] - mainly the decidability for a D0L-language [12] to be strongly repetitive or not. This construction also yields effective symbolic descriptions of the stable sets of curves associated with these automorphisms.