Two Dimensional Prefix Codes of Pictures

Infinite Two-Dimensional Strong Prefix Codes: Characterization and Properties

“…Let us recall the definitions of codes and strong prefix codes of pictures given in [3,4,7,9], together with some examples. Let Σ be a finite alphabet.…”

“…In [4,7], a new definition of picture code was introduced by referring to the operation of tiling star as defined in [24]; the tiling star of a set X is the set X * * of all pictures that are tilable (in the polyominoes style) by elements of X. Then, X is a code if any picture in X * * is tilable in a unique way.…”

“…A first definition of two-dimensional prefix code is proposed in [4,7]. It is based on some special kind of polyominoes that have straight top border.…”

Prefix Picture Codes: A Decidable Class of Two-Dimensional Codes

“…A preliminary version of these results appeared in [3]. Related notions of strong prefix codes and codes with finite deciphering delay are investigated in [4,5].…”

Sets of Pictures Avoiding Overlaps

“…Many researchers have investigated how the notion of recognizability by finite state automata can be transferred to two dimensions to accept picture languages [2, 7-9, 21, 26, 27, 29, 32]. Moreover, two-dimensional codes were studied in different contexts [1,18,22,30] and recently two-dimensional prefix codes were introduced as the two-dimensional counterpart of string prefix codes [3,4,9,11,12].…”