Abstract
Two variants of pebble tree-walking automata on binary trees are considered that were introduced in the literature. It is shown that for each number of pebbles, the two models have the same expressive power both in the deterministic case and in the nondeterministic case. Furthermore, nondeterministic (resp. deterministic) tree-walking automata with n + 1 pebbles can recognize more languages than those with n pebbles. Moreover, there is a regular tree language that is not recognized by any tree-walking automaton with pebbles. As a consequence, FO+posTC is strictly included in MSO over trees.
Work supported by the French-German cooperation programme PROCOPE, KBN Grant 4 T11C 042 25, and the EU-TMR network GAMES.
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© 2006 Springer-Verlag Berlin Heidelberg
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Bojańczyk, M., Samuelides, M., Schwentick, T., Segoufin, L. (2006). Expressive Power of Pebble Automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_15
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DOI: https://doi.org/10.1007/11786986_15
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