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A perfect hashing incremental scheme for unranked trees using pseudo-minimal automata

Rafael C. Carrasco, Jan Daciuk (2009)

RAIRO - Theoretical Informatics and Applications

We describe a technique that maps unranked trees to arbitrary hash codes using a bottom-up deterministic tree automaton (DTA). In contrast to other hashing techniques based on automata, our procedure builds a pseudo-minimal DTA for this purpose. A pseudo-minimal automaton may be larger than the minimal one accepting the same language but, in turn, it contains proper elements (states or transitions which are unique) for every input accepted by the automaton. Therefore, pseudo-minimal DTA...

A periodicity property of iterated morphisms

Juha Honkala (2007)

RAIRO - Theoretical Informatics and Applications

Suppose ƒ : X* → X* is a morphism and u,v ∈ X*. For every nonnegative integer n, let zn be the longest common prefix of ƒn(u) and ƒn(v), and let un,vn ∈ X* be words such that ƒn(u) = znun and ƒn(v) = znvn. We prove that there is a positive integer q such that for any positive integer p, the prefixes of un (resp. vn) of length p form an ultimately periodic sequence having period q. Further, there is a value of q which works for all words u,v ∈ X*.

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