Decidability of Conjugacy of Tree-Shifts of Finite Type

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 shifts, i.e. we show that a conjugacy between two 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 t...

• Type: Conference
• Year: 2009
• Where: ICALP
• Authors: Nathalie Aubrun, Marie-Pierre Béal
• Keywords: Finite Type, ICALP 2009, One-sided Shifts, Theoretical Computer Science, Tree Shifts