On the Power of Tree-Walking Automata

Tree walking automata TWAs recently received new attention in the elds of formal languages and databases Towards a better understanding of their expressiveness we characterize them in terms of transitive closure logic formulas in normal form It is conjectured by Engelfriet and Hoogeboom that TWAs cannot de ne all regular tree languages or equivalently all of monadic second order logic We proof this conjecture for a restricted but powerful class of TWAs In particular we show that bounded TWAs that is TWAs that are only allowed to traverse every edge of the input tree at most once in every direction cannot de ne all regular languages We then extend this result to a class of TWAs that can simulate rst order logic FO and is capable of expressing properties not de nable in FO extended with regular path expressions the latter logic being a valid abstraction of current query languages for XML and semi structured data Research Assistant of the Fund for Scienti c Research Flanders