A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper, we study the shifts of finite type defined by infinite trees. Indeed, infinite trees have a natural structure of one-sided shifts, between the shifts of dimension one and two. We prove a decomposition theorem for these tree-shifts, i.e. we show that a conjugacy between two tree-shifts of finite type can be broken down into a finite sequence of elementary transformations called in-splittings and in-amalgamations. We prove that the conjugacy problem is decidable for tree-shifts of finite type. This result makes the class of tree-shifts closer to the class of one-sided shifts of dimension one than to the class of two-sided ones. Our proof uses the notion of bottom-up tree automata. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Aubrun, N., & Béal, M. P. (2009). Decidability of conjugacy of tree-shifts of finite type. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5555 LNCS, pp. 132–143). https://doi.org/10.1007/978-3-642-02927-1_13
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