Abstract
We consider array languages (sets of picturesconsisting of symbols placed in the lattice points of the 2D grid) and thepossibility to handle them with P systems. After proving binary normal formsfor array matrix grammars (which, even in the case when no appearance checking isused, are known to generate the array languages of arbitrary array grammars), weprove that the P systems with context-free rules (with three membranes and no control on the communication or the use of rules) are computationally universal, able togenerate all computable array languages. Some open problems are also formulated.
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References
Cook CR and Wang PS-P (1978) A Chomsky hierarchy of isotonic array grammars and languages. Computer Graphics and Image Processing 8: 144–152
Dassow J, Freund R and Păun Gh (1995) Cooperating array grammar systems. J Automata, Languages, and Combinatorics 9: 1–25
Dassow J and Păun Gh (1989) Regulated Rewriting in Formal Language Theory. Springer-Verlag, Berlin
Dersanambika KS and Krithivasan K (2003) Contextual array P systems. Submitted
Freund R (1994) Control mechanisms on #-context-free array grammars. In: Păun Gh (ed) Mathematical Aspects of Natural and Formal Languages, pp. 97–137. World Scientific, Singapore
Freund R (2000) Array Grammars. Technical Rep. 15/00, Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, 164 pp
Krishna SN, Krithivasan K and Rama R (2001) P systems with picture objects. Acta Cybernetica 15: 53–74
Maurer H, Rozenberg G and Welzl E (1982) Using string languages to describe picture languages. Information and Control 54: 155–185
Mutyam M (2003) New results in rewriting P systems. New Generation Computing, in press
Păun Gh (2002) Membrane Computing: An Introduction. Springer-Verlag, Berlin, Heidelberg
Rosenfeld A (1979) Picture Languages. Academic Press, Reading, MA
Salomaa A (1973) Formal Languages. Academic Press, New York
Siromoney G, Siromoney R and Krithivasan K (1972) Abstract families of matrices and picture languages. Computer Graphics and Image Processing 1: 284–307
Wang PS-P (1980) Some new results on isotonic array grammars. Information Processing Letters 10: 129–131
Yamamoto Y, Morita K and Sugata K (1989) Context-sensitivity of two-dimensional regular array grammars. In: Wang PS-P (ed) Array Grammars, Patterns and Recognizers, pp. 17–41. WSP Series in Computer Science, Vol. 18, World Scientific Publ, Singapore
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Ceterchi, R., Mutyam, M., Păun, G. et al. Array-rewriting P systems. Natural Computing 2, 229–249 (2003). https://doi.org/10.1023/A:1025497107681
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DOI: https://doi.org/10.1023/A:1025497107681