A decidable characterization of locally testable tree languages
  A regular tree language L is locally testable if membership of a tree in L depends only on the presence or absence of some fix set of neighborhoods in the tree. In this paper we show that it is decidable whether a regular tree language is locally testable. The decidability is shown for ranked trees and for unranked unordered trees. 
Thomas Place (ENS Cachan & INRIA), Luc Segoufin (INRIA & ENS Cachan)
cs.FL