One-visit caterpillar tree automata

Authors:
Alexander Okhotin;Kai Salomaa;Michael Domaratzki
Affiliations:
School of Computing, Queen's University Kingston, Ontario, Canada K7L3N6;School of Computing, Queen's University Kingston, Ontario, Canada K7L3N6;School of Computing, Queen's University Kingston, Ontario, Canada K7L3N6
Venue:
Fundamenta Informaticae
Year:
2002

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Abstract

We study caterpillar tree automata [3] that are restricted to enter any subtree at most one time (or k times). We show that, somewhat surprisingly, the deterministic one-visit automata can already, for instance, evaluate trees where the nodes represent some non-associative operations. We show that there exist regular tree languages that cannot be accepted by a one-visit automaton, thus proving a weakened form of a conjecture of Brüggemann-Klein and Wood [3]. We establish that the k-visit property is decidable.