Annual Report 2010 - Fachgruppe Informatik an der RWTH Aachen ...

Finite Automata on Unranked Trees: Extensions by Arithmetical and Equality
Constraints
Karianto Wong
The notion of unranked trees has attracted much interest in current research, especially due to
their application as formal models of XML documents. In particular, several automata and
logic formalisms on unranked trees have been considered (again) in the literature, and many
results that had previously been shown for the ranked-tree setting have turned out to hold for
the unranked-tree setting as well. In this thesis, we study two kinds of extensions of finite
automata on unranked trees, namely, the extension by arithmetical constraints and the
extension by subtree-equality constraints.
In the first part of the thesis we introduce a framework of automata on unranked trees that
unifies two different approaches to incorporating arithmetical constraints known from the
literature, namely the global-constraint approach of Klaedtke and Rueß (2003) and the localconstraint
approach of Seidl et al. (2003). We investigate the relationship between the two
types of arithmetical constraints with respect to language recognition, and we show that the
emptiness problem for this automaton model is decidable.
In the second part of this thesis, we introduce automata on unranked trees that are equipped
with equality and disequality constraints between direct subtrees, thereby extending the
corresponding automaton model in the ranked-tree setting, which was introduced by Bogaert
and Tison (1982). In the definition of the automaton model, we propose using formulas of
monadic second-order logic to capture the possibility of comparing unboundedly many direct
subtrees for equality, a feature that arises naturally in light of the unrankedness. Our main
result is that the emptiness problem for this automaton model is decidable. Based upon this
result, furthermore, we introduce a logic over data words (that is, words over an infinite
alphabet) for which the satisfiability problem is decidable.
Evaluators: Priv.-Doz. Dr. Christof Löding,
Prof. Dr. Dr.h.c. Wolfgang Thomas,
Prof. Dr. Thomas Schwentick
Date of oral examination: 22 June 2010
497