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The hierarchy of codes

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Fundamentals of Computation Theory (FCT 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 710))

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Abstract

We survey results and problems concerning structural properties of the hierarchy of classes of codes. In particular, we show that abstract dependence systems can be used to gain new insights into hierarchy constructions and decidability proofs. From the same perspective, we also review some work on maximal codes.

This research was supported by the Natural Science and Engineering Research Council of Canada, Grant OGP0000243.

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References

  1. J. Berstel, D. Perrin: Theory of Codes. Academic Press, Orlando, 1985.

    Google Scholar 

  2. V. Bruyère: Maximal Codes with Bounded Deciphering Delay. Theoretical Computer Science 84 (1991), 53–76.

    Article  Google Scholar 

  3. V. Bruyère: Maximal Prefix Products. Semigroup Forum 36 (1987), 147–157.

    Google Scholar 

  4. P. M. Cohn: Universal Algebra. Harper and Row, New York, 1965. Revised edition, D. Reidel Publishing Co., Dordrecht, 1981.

    Google Scholar 

  5. L. J. Cummings: Combinatorics on Words, Progress and Perspectives. Academic Press, Toronto, 1983.

    Google Scholar 

  6. P. H. Day, H. J. Shyr: Languages defined by Some Partial Orders. Soochow J. Math. 9 (1983), 53–62.

    Google Scholar 

  7. C. De Felice, A. Restivo: Some Results on Finite Maximal Codes. RAIRO Inform. Théor. Applicat. 19 (1985), 383–403.

    Google Scholar 

  8. C. De Felice: Construction of a Family of Finite Maximal Codes. Theoretical Computer Science 63 (1989), 157–184.

    Article  Google Scholar 

  9. A. Ehrenfeucht, G. Rozenberg: Each Regular Code is Included in a Maximal Regular Code. RAIRO Inform. Théor. Appiicat. 20 (1985), 89–96.

    Google Scholar 

  10. J. Engelfriet: Iterated Stack Automata and Complexity Classes. Inform. and Computation 95 (1991), 21–75.

    Article  Google Scholar 

  11. J. Engelfriet, H. Vogler: Look-ahead on Pushdowns. Inform. and Computation 73 (1987), 245–279.

    Article  Google Scholar 

  12. J. Engelfriet, H. Vogler: Pushdown Machines for the Macro Tree Transducer. Theoret. Comput. Sci. 42 (1986), 251–368.

    Article  Google Scholar 

  13. J. Engelfriet, H. Vogler: High Level Tree Transducers and Iterated Pushdown Tree Transducers. Acta Inform. 26 (1988), 131–192.

    Google Scholar 

  14. F. Gécseg, H. Jürgensen: Algebras with Dimension. Algebra Universalis, to appear.

    Google Scholar 

  15. F. Gécseg, H. Jürgensen: Dependence in Algebras. Report 239, Dep. Comp. Sci., The University of Western Ontario, 1989.

    Google Scholar 

  16. G. Grätzer: Universal Algebra. D. van Nostrand Co., Princeton, 1968.

    Google Scholar 

  17. L. H. Haines: On Free Monoids Partially Ordered by Embedding. J. Combinatorial Theory 6 (1969), 94–98.

    Google Scholar 

  18. T. Head, A. Weber: Deciding Code Related Properties by Means of Finite Transducers. In: Sequences II, Methods in Communication, Security, and Computer Science, edited by R. Capocelli, A. de Santis, U. Vaccaro. Springer-Verlag, Berlin, 1993, 260–272.

    Google Scholar 

  19. G. Higman: Ordering by Divisibility in Abstract Algebras. Proc. London Math. Soc. 3 (1952), 326–336.

    Google Scholar 

  20. M. Ito, H. Jürgensen, H. J. Shyr, G. Thierrin: Anti-Commutative Languages and n-Codes. Discrete Applied Math. 24 (1989), 187–196.

    Article  Google Scholar 

  21. M. Ito, H. Jürgensen, H. J. Shyr, G. Thierrin: Outfix and Infix Codes and Related Classes of Codes. J. Comput. System Sci. 43 (1991), 484–508.

    Article  Google Scholar 

  22. M. Ito, H. Jürgensen, H. J. Shyr, G. Thierrin: n-Prefix-Suffix Languages. Internat. J. Comp. Math. 30 (1989), 37–56.

    Google Scholar 

  23. M. Ito, H. Jürgensen, H. J. Shyr, G. Thierrin: Languages Whose n-Element Subsets Are Codes. Theoretical Computer Science 96 (1992), 325–344.

    Article  Google Scholar 

  24. M. Ito, H. Jürgensen: Shuffle Relations. Manuscript, in Preparation.

    Google Scholar 

  25. M. P. Jullien: Sur un théorème d'extension dans la théorie des mots. C. R. Acad. Sci. Paris A266 (1968), 651–654.

    Google Scholar 

  26. H. Jürgensen, H. J. Shyr, G. Thierrin: Codes and Compatible Partial Orders. In: Algebra and Order, Proc. 1st International Sympos. on Ordered Algebraic Structures, Luminy-Marseilles, 1984, edited by S. Wolfenstein. Heldermann-Verlag, Berlin, 1986, 323–333.

    Google Scholar 

  27. H. Jürgensen, S. S. Yu: Solid Codes. EIK 26 (1990), 563–574.

    Google Scholar 

  28. H. Jürgensen, G. Thierrin: Infix Codes. Topics in the Theoretical Bases and Applications of Computer Science, Proc. 4th Hungarian Comp. Sci. Conf., Györ, 1985, edited by M. Arató, I. Kátai, L. Varga. Akadémiai Kiadó, Budapest, 1986, 25–29.

    Google Scholar 

  29. H. Jürgensen, S. S. Yu: Dependence Systems and Hierarchies of Families of Languages. Manuscript, in Preparation

    Google Scholar 

  30. H. Jürgensen: Syntactic Monoids of Codes. Report 327, Dep. Comp. Sci., The University of Western Ontario, 1992.

    Google Scholar 

  31. H. Jürgensen, K. Salomaa, S. Yu: Transducers and the Decidability of Independence in Free Monoids. Report 329, Dep. Comp. Sci., The University of Western Ontario, 1992.

    Google Scholar 

  32. H. Jürgensen, S. S. Yu: Relations on Free Monoids, Their Independent Sets, and Codes. Internat. J. Computer Math. 40 (1991), 17–46.

    Google Scholar 

  33. H. Jürgensen, M. Katsura, S. Konstantinidis: Maximal Solid Codes. Manuscript, in Preparation, 1993.

    Google Scholar 

  34. H. Jürgensen, K. Salomaa, S. Yu: Decidability of the Intercode Property. Report 349, Dep. Comp. Sci., The University of Western Ontario, 1993.

    Google Scholar 

  35. J. Karhumäki: On Three-Element Codes. In: Proceedings ICALP 1984, edited by J. Paredaens. Lecture Notes in Computer Science 172, Springer-Verlag, Berlin, 1984, 292–302.

    Google Scholar 

  36. Dongyang Long: n-infix-outfix codes. In: Abstracts, Second International Colloquium on Words, Languages, and Combinatorics, Kyoto, 1992, 50–51.

    Google Scholar 

  37. Dongyang Long: k-Outfix Codes. Chinese Annals of Math. 10A (1989), 94–99 (in Chinese).

    Google Scholar 

  38. Dongyang Long: k-Prefix Codes and k-Infix Codes. Acta Math. Sinica 33 (1990), 414–421 (in Chinese).

    Google Scholar 

  39. M. Lothaire: Combinatorics on Words. Addison-Wesley Publishing Company, London, 1983.

    Google Scholar 

  40. M. Petrich, G. Thierrin: The Syntactic Monoid of an Infix Code. Proc. Amer. Math. Soc. 109 (1990), 865–873.

    Google Scholar 

  41. A. Restivo: On Codes Having no Finite Completions. Discrete Math. 17 (1977), 309–316.

    Article  Google Scholar 

  42. A. Restivo, S. Salemi, T. Sportelli: Completing Codes. RAIRO Inform. Théor. Applicat. 23 (1989), 135–147.

    Google Scholar 

  43. M. Satyanarayana, S. Mohanty: Uniformly Synchronous Limited Codes. Semigroup Forum 46 (1993), 21–26.

    Google Scholar 

  44. M. Satyanarayana: Uniformly Synchronous Codes. Semigroup Forum 46 (1993), 246–252.

    Google Scholar 

  45. H. J. Shyr: Free Monoids and Languages. Second Edition, Hon Min Book Company, Taichung, Taiwan, 1991.

    Google Scholar 

  46. H. J. Shyr, G. Thierrin: Codes and Binary Relations. Séminaire d'algèbre Paul Dubreil, Paris 1975–1976, (29ème Année). Edited by M. P. Malliavin. Lecture Notes in Mathematics 586, Springer-Verlag, Berlin, 1977, 180–188.

    Google Scholar 

  47. H. J. Shyr, G. Thierrin: Hypercodes. Information and Control 24 (1974), 45–54.

    Article  Google Scholar 

  48. H. J. Shyr, S. S. Yu: Intercodes and Some Related Properties. Soochow J. of Math. 16 (1990), 95–107.

    Google Scholar 

  49. L. Staiger: On Infinitary Finite Length Codes. RAIRO Inform. Theor. Applicat. 20 (1986), 483–494.

    Google Scholar 

  50. G. Thierrin: The Syntactic Monoid of a Hypercode. Semigroup Forum 6 (1973), 227–231.

    Google Scholar 

  51. G. Thierrin, S. S. Yu: Shuffle Relations and Codes. J. Inform. and Optim. Sci. 12 (1991), 441–449.

    Google Scholar 

  52. E. Valkema: Syntakische Monoide und Hypercodes. Semigroup Forum 13 (1976/77), 119–126.

    Google Scholar 

  53. M. Vincent: Construction de codes indécomposables. RAIRO Inform. Théor. Applicat. 19 (1985), 165–178.

    Google Scholar 

  54. D. J. A. Welsh: Matroid Theory. Academic Press, London, 1976.

    Google Scholar 

  55. D. Wood: Theory of Computation. Harper & Row, New York, 1987.

    Google Scholar 

  56. S. S. Yu: Codes and n-ary Relations. Ph. D. Thesis, The University of Western Ontario, 1990.

    Google Scholar 

  57. S. S. Yu: A Characterization of Intercodes. Internat. J. Comp. Math. 36 (1990), 39–45.

    Google Scholar 

  58. S. Zhang: An Equivalence Relation on Suffix Codes Defined by Generalized Regular Languages. Internat. J. Comp. Math. 35 (1990), 15–24.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    H. Jürgensen & S. Konstantinidis

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  1. H. Jürgensen
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  2. S. Konstantinidis
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Zoltán Ésik

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© 1993 Springer-Verlag Berlin Heidelberg

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Jürgensen, H., Konstantinidis, S. (1993). The hierarchy of codes. In: Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 1993. Lecture Notes in Computer Science, vol 710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57163-9_4

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  • DOI: https://doi.org/10.1007/3-540-57163-9_4

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  • Print ISBN: 978-3-540-57163-6

  • Online ISBN: 978-3-540-47923-9

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