From Determinism to Non-determinism in Recognizable Two-Dimensional Languages

Snake-Deterministic Tiling Systems

“…Let L frames = L f r= f c ∩L lr=lc ∩L 2 f r=2lc ∩L 2lr=2 f c be the language of square pictures such that: the first row equals the first column, the last row equals the last column, the second row equals the reverse of the second last column, the second last row equals the reverse of the second column. Then L frames is in UREC but not in Diag-DREC [1].…”

“…Here we present the notion of determinism proposed in [1]. This is inspired by the deterministic version of online tessellation acceptors [9], which are directed according to a corner-to-corner direction (namely, from top-left to bottom-right, or tl2br).…”

“…In [1] a hierarchy of classes between determinism and unambiguity is also exhibited. Here we adapt the basic definitions, results, and examples from [1].…”

“…UREC defines unambiguously tiling recognizable languages, whose pictures are the projection of a unique element in the corresponding local language. In an effort to go towards determinism, the authors of [1] introduced an intermediate notion of "line" unambiguity, embodied in classes Row-UREC and Col-UREC, and based on backtracking at most linear in one dimension of the picture.…”

“…the classes defined by deterministic 4-way automata [10] or deterministic online tessellation automata [9]. This latter model inspired the notion of determinism of [1], that relies on four diagonal-based scanning strategies, each starting from one of the four corners of the picture. To mark this aspect, in this paper we will call the corresponding deterministic class Diag-DREC 1 .…”