Handbook of theoretical computer science (vol. B)
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Tree Automata and Languages
Sofic and almost of finite type tree-shifts
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Theoretical Computer Science
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 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.