Loops and overloops for Tree-Walking Automata

Tree-Walking Automata (TWA) have lately received renewed interest thanks to their tight connection to XML. This paper introduces the notion of tree overloops, which is closely related to tree loops, and investigates the use of both for the following common operations on TWA: testing membership, transformation into a Bottom-Up Tree Automaton (BUTA), and testing emptiness. Notably, we argue that the transformation into a BUTA is slightly less straightforward than was previously assumed, show that using overloops yields much smaller BUTA in the deterministic case, and provide a polynomial over-approximation of this construction which detects emptiness with surprising accuracy against randomly generated TWA.