Abstract
We study some properties of axray grammars, called puzzle grammars, introduced in [NS89].We give a new method, using puzzle grammar, for generating the set of rectangles. We prove the the emptiness problem for puzzle grammar is undecidable. We show that the non-overlapping problem for puzzle grammar is decidable.
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Danielle Beauquier, An undecidable problem about rationnal sets and contour words of polyominoes, Inf. Process. Letters. Vol 37 n 5 (March 1991), 257–263.
D. Beauquier, M. Nivat, About rationnal subset of algebras of infinite words, in Automata, Languages and programming (W. Brauer ed.), LNCS, u 192, Springer-Verlag, Berlin (1985) 33–42.
C.R. Cook and P.S.P. Wang, Chomsky hierarchy of isotonic array grammars and languages, Computer Graphics and Image Proccesing 8(1978) 144–152.
K. Inoue, I. Sakuramoto, M. Sakamoto and I. Takanami, Two Topics concerning Two-dimensionnal Automata Operating in Parallel, Proc. of the First Int. Conf. on Parallel Image Processing, (1991) 231–262.
K. Morita, Y. Yamamoto and K. Sugata, The Complexity of some Decision Problems about Array Grammars, Inf. Sciences, 30 (1983)241–262.
M.Nivat, A. Saoudi, K.G. Subramanian, R. Siromoney and V.R. Dare, Puzzle Grammars and Context-Free Array Grammars, Int. J. of Pattern Recognition and Art. Int., vol 5, n 5 (1992) 663–675.
M. Nivat, A. Saoudi, Notes on Puzzle Grammars, unpublished (1989).
M. Nivat, A. Saoudi,Parallel Recognition of High Dimensionnal Images, Proc. of the First Int. Conf. on Parallel Image Processing, (1991) 123–130.
W.Rytter, A. Saoudi,Pn parallel Recognition of Two Classes of 2D-Array Patterns, Proc. of the First Int. Conf. on Parallel Image Processing, (1991) 153–160.
A. Rosenfeld, Isotonic Grammars, Parallel Grammars and Picture Languages, in Machine Intelligence (B. Meltzer and D. Michie, Eds), Univ. of Edinburgh Press (1971)
A. Rosenfeld, Array Grammars normal forms, Informations and Control 23(1973)173–182
A. Rosenfeld, Picture languages: formal models for picture recognition, Academic Press 1979.
Y. Yamamoto, K.Morita and K. Sutaga, Context-sensitivity of two-dimentionnal regular array grammars, Int. J. of Pattern Recognition and Art. Int. vol. 3&4 (1989)295–320.
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© 1992 Springer-Verlag Berlin Heidelberg
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Laroche, P., Nivat, M., Saoudi, A. (1992). Context-sensitivity of puzzle grammars. In: Nakamura, A., Nivat, M., Saoudi, A., Wang, P.S.P., Inoue, K. (eds) Parallel Image Analysis. ICPIA 1992. Lecture Notes in Computer Science, vol 654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56346-6_39
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DOI: https://doi.org/10.1007/3-540-56346-6_39
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