Variable Tree Automata over Infinite Ranked Alphabets

Abstract

We introduce variable tree automata with infinite input ranked alphabets. Our model is based on an underlying bottom-up tree automaton over a finite ranked alphabet containing variable symbols. The underlying tree automaton computes its tree language, and then replaces the variable symbols with symbols from the infinite alphabet following certain rules. We show that the class of recognizable tree languages over infinite ranked alphabets is closed under union and intersection but not under complementation. The emptiness problem is decidable, and the equivalence problem is decidable within special subclasses of variable tree automata. The universality problem is also decidable in a subclass of variable tree automata. We demonstrate the robustness of our model by connecting it to variable finite automata and indicating several characterizations of recognizable tree languages over infinite ranked alphabets.