Deciding Twig-definability of Node Selecting Tree Automata

Abstract

Node selecting tree automata (NSTAs) constitute a general formalism defining unary queries over trees. Basically, a node is selected by an NSTA when it is visited in a selecting state during an accepting run. We consider twig patterns as an abstraction of XPath. Since the queries definable by NSTAs form a strict superset of twig-definable queries, we study the complexity of the problem to decide whether the query by a given NSTA is twig-definable. In particular, we obtain that the latter problem is EXPTIME-complete. In addition, we show that it is also EXPTIME-complete to decide whether the query by a given NSTA is definable by a node selecting string automaton.

A Note on Decidable Separability by Piecewise Testable Languages

“…There were many more results showing that, for regular languages and subclasses thereof, often corresponding to a logical fragment, the problem is decidable (see for example Brzozowski and Simon, 1971;Zalcstein, 1972;McNaughton, 1974;Knast, 1983;Arfi, 1987;Pin and Weil, 1997;Straubing, 1988;Thérien and Wilke, 1998;Glaßer and Schmitz, 2000;Tesson and Thérien, 2002;Klíma, 2011;Czerwiński et al, 2013a;Zeitoun, 2014a, 2017;Place, 2015b;Almeida et al, 2015). Similar problems have been considered for trees (Bojańczyk and Idziaszek, 2009;Benedikt and Segoufin, 2009;Bojańczyk et al, 2012;Antonopoulos et al, 2012;Place and Segoufin, 2015).…”