A note on partially ordered tree automata

Abstract

A recent paper by Bouajjani, Muscholl and Touili shows that the class of languages accepted by partially ordered word automata (or equivalently accepted by Σ 2 -formulae) is closed under semi-commutation and it suggested the following open question: can we extend this result to tree languages? This problem can be addressed by proving (1) that the class of tree regular languages accepted by Σ 2 formulae is strictly included in the class of languages accepted by partially ordered automata, and (2) that Bouajjani and the others results cannot be extended to tree.We assume the reader is familiar with the basic notions on terms and tree automata. For general reference see [6].