Abstract.
The notion of shuffle on trajectories is a natural generalization of many word operations considered in the literature. For a set of trajectories T, we define the notion of a T-code and examine its properties. Particular instances of T-codes are prefix-, suffix-, infix-, outfix- and hyper-codes, as well as other classes studied in the literature.
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References
Berstel, J., Perrin, D. (1996) Theory of codes. Available at http://www-igm.univ-mlv.fr/%7Eberstel/LivreCodes/Codes.html
Bruyére, V., Perrin, D. (1999) Maximal bifix codes. Theor. Comput. Sci. 218: 107-121
Choffrut, C., Karhumäki, J. (1997) Combinatorics on words. In: [36], pp. 329-438
Conway, J. (1971) Regular algebra and finite machines. Chapman and Hall
de Luca, A., Varricchio, S. (1997) Regularity and finiteness conditions. In: [36], pp. 747-810
Domaratzki, M. (2004) Deletion along trajectories. Theor. Comp. Sci. (accepted)
Domaratzki, M. (2004) Trajectory-based embedding relations. Fund. Inf. (accepted)
Ehrenfeucht, A., Haussler, D., Rozenberg, G. (1983) On regularity of context-free languages. Theor. Comput. Sci. 23: 311-332
Flajolet, P., Steyaert. J.-M. (1974) On sets having only hard subsets. In: Loeckx, J. (ed.) Automata languages and programming. Lecture Notes in Computer Science, Vol. 14, pp. 446-457.
Ginsburg, S. (1966) The mathematical theory of context-free languages. McGraw-Hill
Guo, Y., Shyr, H., Thierrin, G. (1986) E-convex infix codes. Order 3: 55-59
Haines, L. (1969) On free monoids partially ordered by embedding. J. Comb. Theory 6: 94-98
Harju, T., Ilie, L. (1998) On quasi orders of words and the confluence property. Theor. Comput. Sci. 200: 205-224
Harrison, M. (1978) Introduction to formal language theory. Addison-Wesley
Higman, G. (1952) Ordering by divisibility in abstract algebras. Proc. Lond. Math. Soc. 2(3): 326-336
Hopcroft, J.-E., Ullman, J.-D. (1979) Introduction to automata theory, languages, and computation. Addison-Wesley
Ilie, L., Salomaa, A. (1998) On well quasi orders of free monoids. Theor. Comput. Sci. 204: 131-152
Ilie, L. (1997) Remarks on well quasi orders of words. In: Bozapalidis, S. (ed.) Proceedings of the 3rd DLT, pp. 399-411
Ilie, L. (1998) Decision problems on orders of words. PhD thesis, University of Turku
Ito, M., Jürgensen, H., Shyr, H., Thierrin, G. (1991) Outfix and infix codes and related classes of languages. J. Comput. Syst. Sci. 43: 484-508
Jullien, P. (1968) Sur un théoréme d’extension dans la théorie des mots. C. R. Acad. Sci., Paris, Sér. A 266: 851-854 (1968)
Jürgensen, H., Konstantinidis, S. (1997) Codes. In: [36], pp. 511-600
Jürgensen, H., Shyr, H., Thierrin, G. (1984/1986) Codes and compatible partial orders on free monoids. In: Wolfenstein, S. (ed.) Algebra and order: Proceedings of the First International Symposium on Ordered Algebraic Structures, Luminy-Marseilles 1984, pp. 323-334. Heldermann Verlag
Jürgensen, H., Yu, S.S. (1991) Relations on free monoids, their independent sets, and codes. Int. J. Comput. Math. 40: 17-46
Kadrie, A., Dare, V., Thomas, D., Subramanian, K. (2001) Algebraic properties of the shuffle over \(\omega\)-trajectories. Inf. Process. Letters 80(3): 139-144
Kari, L., Konstantinidis, S., Sosík, S. (2003) On properties of bond-free DNA languages. Technical Report 609, Computer Science Department, University of Western Ontario (submitted for publication)
Kari, L., Sosík, P. (2003) Language deletions on trajectories. Technical Report 606, Computer Science Department, University of Western Ontario (submitted for publication)
Kari, L., Thierrin, G. (1995) k-catenation and applications: k-prefix codes. J. Inf. Optimization Sci. 16(2): 263-276
Kari, L. (1994) On language equations with invertible operations. Theor. Comput. Sci. 132: 129-150
Kruskal, J. (1972) The theory of well-quasi-ordering: A frequently discovered concept. J. Comb. Theory, Ser. A 13: 297-305
Lam, N. (2000) Finite maximal infix codes. Semigroup Forum 61: 346-356
Long, D. (1993) On two infinite hierarchies of prefix codes. In: Shum, K., Yuen, P. (eds.) Proceedings of the Conference on Ordered Structures and Algebra of Computer Languages, pp. 81-90. World Scientific
Long, D. (1994) k-bifix codes. Rivista di Matematica Pura ed Applicata 15: 33-55
Lothaire, M. (1983) Combinatorics on words. Addison-Wesley
Mateescu, A., Rozenberg, G., Salomaa, A. (1998) Shuffle on trajectories: Syntactic constraints. Theor. Comput. Sci. 197: 1-56
Rozenberg, G., Salomaa, A. (eds.) (1997) Handbook of formal languages, Vol. I. Heidelberg Berlin New York: Springer
Shyr, H., Thierrin, G. (1974) Hypercodes. Inf. Control 24(1): 45-54
Shyr, H., Thierrin, G. (1977) Codes and binary relations. In: Dold, A., Eckmann, B. (eds.) Séminaire d’Algébre Paul Dubreil, Paris 1975-1976. Lecture Notes in Mathematics, Vol. 586, pp. 180-188. Berlin Heidelberg New York: Springer
Shyr, H. (2001) Free monoids and languages. Taichung, Taiwan: Hon Min Book Compan
Sloane, N. (2004) The on-line encyclopedia of integer sequences. Published electronically at http://www.research.att.com/~njas/sequences
Thierrin G., Yu, S.S. (1991) Shuffle relations and codes. J. Inf. Optimization Sci. 12(3): 441-449
Thierrin, G. (1972) Convex languages. In: Nivat, M. (ed.) Automata, languages and programming, pp. 481-492. Amsterdam: North-Holland
van Leeuwen, J. (1978) Effective constructions in well-partially ordered free monoids. Discrete Math. 21: 237-252
Yu, S. (1997) Regular languages. In: [36], pp. 41-110
Zhang, L., Shen, Z. (1995) Completion of recognizable bifix codes. Theor. Comput. Sci. 145: 345-355
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Received: 1 December 2003, Published online: 25 March 2004
Research supported in part by an NSERC PGS-B graduate scholarship.
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Domaratzki, M. Trajectory-based codes. Acta Informatica 40, 491–527 (2004). https://doi.org/10.1007/s00236-004-0140-4
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DOI: https://doi.org/10.1007/s00236-004-0140-4