On factors of synchronized sequences
Let k >= 2 be an integer. A sequence of natural numbers is k-synchronized if its graph is represented, in base k, by a right-synchronized rational relation. We show that the factor complexity and the palindromic complexity of a k-synchronized sequence are k-regular sequences. We derive that the palindromic complexity of a k-automatic sequence is k-automatic. (C) 2010 Elsevier B.V. All rights reserved.
synchronized sequence factor complexity palindromic complexity automatic sequence