Z-Automata for Compact and Direct Representation of Unranked Tree Languages

Johanna Björklund, Frank Drewes, Giorgio Satta

Abstract: Unranked tree languages are valuable in natural language processing for modelling dependency trees. We introduce a new type of automaton for unranked tree languages, called Z-automaton, that is tailored for this particular application. The Z-automaton offers a compact form of representation, and unlike the closely related notion of stepwise automata, does not require a binary encoding of its input. We establish an arc-factored normal form, and prove the membership problem of Z-automata in normal form to be in $$ O \left( mn \right) $$ , where m is the size of the transition table of the Z-automaton and n is the size of the input tree.