The Regularity of Two-Way Nondeterministic Tree Automata Languages

We establish that regularly extended two-way nondeterministic tree automata with un-ranked alphabets have the same expressive power as regularly extended nondeterministic tree automata with unranked alphabets. We obtain this result by establishing regularly extended versions of a congruence on trees and of a congruence on, so called, views. Our motivation for the study of these tree models is the Extensible Markup Language (XML), a metalanguage for deening document grammars. Such grammars have regular sets of right-hand sides for their productions and tree automata provide an alternative and useful modeling tool for them. In particular, we believe that they provide a useful computational model for what we call caterpillar expressions.