Deterministic two-dimensional languages over one-letter alphabet

Abstract

We study the family DREC(1) of deterministic tiling recognizable two-dimensional languages in the case of a one-letter alphabet. The family coincides with both the class of languages accepted by deterministic on-line tessellation acceptors (ℒ(DOTA)(1)) and the one of languages recognized by 2-way alternating finite automata (ℒ(2AFA)(1)). We show that DREC(1) is complex enough to contain languages that cannot be realized by classical operations, while other languages constructed using classical operations cannot be deterministically recognized. Furthermore we prove that there are unambiguously recognizable languages that cannot be deterministically recognized even in the case of one-letter alphabet. In particular ℒ(DOTA)(1) is different from ℒ(OTA)(1) (its non-deterministic counterpart). © Springer-Verlag Berlin Heidelberg 2007.