Tree-Walking Pebble Automata

Abstract

this paper is to investigate the power of tree-walking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use of pebbles, in the sense that the life times of pebbles, i.e., the times between dropping a pebble and lifting it again, are properly nested. A similar, but stronger, nesting requirement is studied in [13] for 2-way automata on strings. We prove in Section 5 that our restriction indeed guarantees that all tree languages recognized by the tree-walking pebble automaton are regular, but we conjecture that the automaton is not powerful enough to recognize all regular tree languages. In Section 6 we generalize the notion of pebble to that of a \set-pebble", in such a way that the tree-walking set-pebble automaton recognizes exactly the regular tree languages.