Abstract In this paper authors study and investigate the shuffle on trajectories on infinite array languages. Like finite array languages this approach is applicable to concurrency providing a method to define parallel composition of processes. It is also applicable to parallel computation. The operations are introduced using a uniform method based on the notion of - trajectory. Authors introduce an Array Grammar with Shuffle on Trajectories (AGST) and compare it with other array grammars for generative poauthorsr. Authors prove closure properties for different classes of array languages with respect to the shuffle on trajectories.

References

[1] Arulprakasam R., Dare V., Gnanasekaran S., and Radhakrishnan M., “Local -Partial Languages,” in Proceedings of National Seminar on Algebra and Analysis Gateway to Modern Technology, Kodambakkam, pp. 69-73, 2013.

[2] Chandra P., Martin-Vide C., Subramanian K., Van D., and Wang P., Handbook of Pattern Recognition and Computer Vision, World Scientific, 2004.

[3] Chandra P., Subramanian K., and Thomas D., “Parallel Contextual Array Grammars and Languages,” Electronic Notes in Discrete Mathematics, vol. 12, pp.106-117, 2000.

[4] Christy D., Masilamani V., Thomas D., Atulya K., Nagar A., and Thamburaj R., “Shuffle on Array Languages Generated by Array Grammars,” Math Application, vol. 3, pp. 17-31, 2014.

[5] Dare V., Annadurai S., Kalyani T., and Thomas D., “Partial Trajectories” in Proceedings on National Conference of Mathematical and Computational Models, Narosa Publications, pp. 418-426, 2007.

[6] Dare V., Annadurai S., Kalyani T., and Thomas D., “Trajectories P Systems,” Progress in Natural Sciences, vol. 18, no. 5, pp. 611-616, 2008.

[7] Dare V., Subramanian K., Thomas D., and Siromoney R., “Infinite Arrays and Recognisability,” International Journal of Pattern Recognition and Artificial Intelligence, vol. 14, no. 4, pp. 525-536, 2000.

[8] Geetha H., Thomas D., Kalyani T., and Venkatesan A., “Shuffle on Trajectories Over Finite Array Languages,” in Proceedings of International Workshop on Combinatorial Image Analysis, Madrid, pp. 261-274, 2011.

[9] Giammaresi D. and Restivo A., Handbook of Formal Languages, Springer-Verlag, 1997.

[10] Jansirani N. and Dare V., “A Study on Diminishing Cells Infinite Array,” in Proceedings of 6th International Conference on Bio-Inspired Computing: Theories and Applications, Penang, pp. 329-332, 2011.

[11] Kadrie A., Dare V., Thomas D., and Subramanian K., “Algebraic Properties of The Shuffle Over Omega Trajectories,” Information Processing Letters, vol. 80, no. 3, pp. 139-144, 2001.

[12] Matescu A., Rozenberg G., and Salomaa A., “Shuffle on Trajectories Systactic Constraints,” Theoretical Computer Science, vol. 197, no. 1-2, pp. 1-56, 1998.

[13] Nakamura A. and Ono H., “Pictures of Functions and their Acceptability by Automata,” Theoretical Computer Science, vol. 23, no. 1, pp. 37-48, 1988.

[14] Park D., “Concurrency and Automata on Infinite Sequences,” in Proceedings of Theoretical Computer Science, Karlsruhe, pp. 167-183, 1981.

[15] Perrin D. and Pin J., “Mots Infinis,” Report LITP, Institut Blaise Pascal, 1993.

[16] Samira C. and Selma B., “Unmanned Vehicle Trajectory Tracking By Neural Networks,” The International Arab Journal of Information Technology, vol. 13, no. 3, pp. 272-275, 2016.

[17] Siromoney R., Dare V., and Subramanian K., “Infinite Arrays and Infinite Computations,” Theoretical Computer Science, vol. 24, no. 2, pp. 195-205, 1983.

[18] Siromoney R., Subramanian K., and Dare V., “On Infinite Arrays Obtained By Deterministic Controlled Table L-Array Systems,” Theoretical Computer Science, vol. 33, pp. 3-11, 1984.

[19] Thomas W., Handbook of Theoretical Computer Science, MIT Press, 1990. Devi Velayutham, M.Sc., M.Phil., B.Ed., Research Scholar, Sathyabama University, Chennai, India. She has 15 years of teaching experience in engineering colleges. Her research interest is automata theory and theory of computations.