Snake-Deterministic Tiling Systems

The concept of determinism, while clear and well assessed for string languages, is still matter of research as far as picture languages are concerned. We introduce here a new kind of determinism, called snake, based on the boustrophedonic scanning strategy, that is a natural scanning strategy used by many algorithms on 2D arrays and pictures. We consider a snake-deterministic variant of tiling systems, which defines the so-called Snake-DREC class of languages. Snake-DREC properly extends the more traditional approach of diagonal-based determinism, used e.g. by deterministic tiling systems, and by online tessellation automata. Our main result is showing that the concept of snake-determinism of tiles coincides with row (or column) unambiguity.