Abstract
Algebraic characterization of recognizable trace languages were studied and the relation of recognizable trace languages to elementary Petri nets were established by using partial commutation as a tool. Motivated by the above studies in string languages, we have extended the notion of partial commutation to two-dimensional array languages and established that if L is local then φ(L) need not be local, where φ is a partial commutation mapping. We have proved that L(φ(θ)) and φ(L(θ)) are not disjoint, where θ is a finite set of 2 ×2 tiles over the alphabet Γ ∪ {#}. We have also considered partial commutation mapping on Siromoney matrix languages and proved some interesting results.
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References
Blum, M., Hewitt, C.: Automata on a 2-dimensional tape. In: Proceedings of IEEE Symposium on Switching and Automata Theory, pp. 155–160 (1967)
Cartier, P., Foata, D.: Problemes combinatories de commutation et rearrangement. Lecture Notes in Mathematics, vol. 85. Springer, Heidelberg (1969)
Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific Publishers, Singapore (1995)
Giammarresi, D., Restivo, A.: Recognizable picture languages. International Journal on Pattern Recognizition and Artificial Intelligence; Nivat, M., Soudi, A., Wang, P.S.P. (eds.) Special Issue on Parallel Image Processing, pp. 31–46 (1992)
Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Handbook of Formal Languages, vol. 3, pp. 215–226. Springer, Berlin (1997)
Mazurkiewicz, A.: Introduction to Trace Theory. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, pp. 3–41. World Scientific Publishers, Singapore (1995)
Ochmański, E.: Recognizable trace languages. In: Diekert, V., Rozenberg, G. (eds.) The Book of Traces, ch. 6, pp. 167–204. World Scientific Publishers, Singapore (1995)
Rosenfeld, A.: Picture languages: Formal Models for Picture Recognition. Academic Press (1979)
Rosenfeld, A., Siromoney, R.: Picture languages - A survey. Languages of Design 1, 229–245 (1993)
Siromoney, G., Siromoney, R., Krithivasan, K.: Abstract families of matrices and picture languages. Computer Graphics and Image Processing 2, 284–307 (1972)
Siromoney, R., Subramanian, K.G., Rangarajan, K.: Parallel/sequential rectangular arrays with tables. International Journal of Computer Mathematics 6A, 143–158 (1977)
Subramanian, K.G.: P Systems and Picture Languages. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 99–109. Springer, Heidelberg (2007)
Thomas, W.: On Logics, Tilings and Automata. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 441–453. Springer, Heidelberg (1991)
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Kamaraj, T., Thomas, D.G., Geetha, H., Kalyani, T. (2012). Partial Commutation on Array Languages. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds) Combinatorial Image Analaysis. IWCIA 2012. Lecture Notes in Computer Science, vol 7655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34732-0_15
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DOI: https://doi.org/10.1007/978-3-642-34732-0_15
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