Abstract
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.
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Brocchi, S., Frosini, A., Pinzani, R., Rinaldi, S.: A tiling system for the class of L-convex polyominoes. Theor. Comput. Sci. 475, 73–81 (2013)
Castiglione, G., Restivo, A.: Reconstruction of l-convex polyominoes. Electronic Notes in Discrete Mathematics 12, 290–301 (2003). 9th International Workshop on Combinatorial Image Analysis
Giammarresi, D., Restivo, A.: Recognizable picture languages. International Journal of Pattern Recognition and Artificial Intelligence 6(02n03), 241–256 (1992)
Smith III, A.R.: Real-time language recognition by one-dimensional cellular automata. Journal of the ACM 6, 233–253 (1972)
Terrier, V.: Two-dimensional cellular automata recognizer. Theor. Comput. Sci. 218(2), 325–346 (1999)
von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Urbana (1966)
Wang, H.: Proving theorems by pattern recognition II. Bell System Technical Journal 40, 1–42 (1961)
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Grandjean, A., Poupet, V. (2015). L-Convex Polyominoes Are Recognizable in Real Time by 2D Cellular Automata. In: Kari, J. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2015. Lecture Notes in Computer Science(), vol 9099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47221-7_10
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DOI: https://doi.org/10.1007/978-3-662-47221-7_10
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