Handbook of theoretical computer science (vol. B)
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Conjugacy of Z2-subshifts and textile systems
Publications of the Research Institute for Mathematical Sciences
On the Finite Degree of Ambiguity of Finite Tree Automata
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
Decidability of Conjugacy of Tree-Shifts of Finite Type
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Elements of Automata Theory
Sofic and almost of finite type tree-shifts
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Theory of Computing Systems
Theory of Computing Systems
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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 ranked trees. Indeed, infinite ranked trees have a natural structure of symbolic dynamical systems. We prove a Decomposition Theorem for these tree-shifts, i.e. we show that a conjugacy between two tree-shifts 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 sequences than to the class of two-sided ones. Our proof uses the notion of bottom-up tree automata.