A polyomino is said to be L-convex if any two of its cells are connected by a
4-connected inner path that changes direction at most once. The 2-dimensional
language representing such polyominoes has been recently proved to be
recognizable by tiling systems by S. Brocchi, A. Frosini, R. Pinzani and S.
Rinaldi. In an attempt to compare recognition power of tiling systems and
cellular automata, we have proved that this language can be recognized by
2-dimensional cellular automata working on the von Neumann neighborhood in real
time.
Although the construction uses a characterization of L-convex polyominoes
that is similar to the one used for tiling systems, the real time constraint
which has no equivalent in terms of tilings requires the use of techniques that
are specific to cellular automata