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Automata for Codes

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Implementation and Application of Automata (CIAA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7982))

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Abstract

We survey the actual and potential rôles of automata in the modelling of information transmission systems and, in particular, in the encoder, channel and decoder components of such systems. Our focus is on applications of codes in such systems and on the relevance of automaton theoretic methods to these applications. We discuss, for example, the issues of error-detection, fault-tolerance and error-correction for variable-length codes. Beyond reviewing known work in a possibly new setting, we also present some recent results on fault-tolerant decoders for systems in which synchronization errors are likely. We conclude with a kind of research programme, a list of rather general open problems requiring solutions.

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References

  1. Béal, M.-P., Berstel, J., Marcus, B.H., Perrin, D., Reutenauer, Ch., Siegel, P.H.: Variable length codes and finite automata. In: Woungang, I., Misra, S., Misra, S.C. (eds.) Selected Topics on Information and Coding Theory. Series on Coding Theory and Cryptology, vol. 7, pp. 505–584. World Scientific, Singapore (2010)

    Google Scholar 

  2. Berstel, J.: Transductions and Context-Free Languages. Leitfäden der angewandten Mathematik und Mechanik, LAMM, vol. 38. B. G. Teubner, Stuttgart (1979)

    Book  MATH  Google Scholar 

  3. Berstel, J., Perrin, D.: Theory of Codes. Academic Press, Orlando (1985)

    MATH  Google Scholar 

  4. Berstel, J., Perrin, D., Reutenauer, Ch.: Codes and Automata. Encyclopedia of Mathematics and Its Applications, vol. 129. Cambridge University Press, Cambridge (2010)

    Google Scholar 

  5. Duske, J., Jürgensen, H.: Codierungstheorie. BI Wissenschaftsverlag, Mannheim (1977)

    MATH  Google Scholar 

  6. Forney Jr., G.D.: The Viterbi algorithm. Proc. IEEE 61(3), 268–278 (1973)

    Article  MathSciNet  Google Scholar 

  7. Glebskii, Y.V.: Coding by means of finite automata. Dokl. Akad. Nauk. SSSR 141, 1054–1057 (1961) (in Russian); English translation: Soviet Physics Dokl. 6, 1037–1039 (1962)

    Google Scholar 

  8. Guiaşu, S.: Information Theory with Applications. McGraw-Hill, New York (1977)

    Google Scholar 

  9. Han, Y.-S., Salomaa, K.: Overlap-free languages and solid codes. Internat. J. Foundations Comput. Sci. 22, 1197–1209 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ito, M., Jürgensen, H., Shyr, H.J., Thierrin, G.: Outfix and infix codes and related classes of languages. J. Comput. System Sci. 43, 484–508 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jégou, H., Malinowski, S., Guillemot, C.: Trellis state aggregation for soft decoding of variable length codes. In: Proceedings of the 2005 IEEE Workshop on Signal Processing Systems: Design and Implementation (SIPS 2005), Athens, Greece, November 2-4, pp. 603–608. IEEE, Piscataway (2005)

    Chapter  Google Scholar 

  12. Jürgensen, H.: Syntactic monoids of codes. Acta Cybernet. 14, 117–133 (1999)

    MathSciNet  MATH  Google Scholar 

  13. Jürgensen, H., Katsura, M., Konstantinidis, S.: Maximal solid codes. J. of Automata, Languages and Combinatorics 6, 25–50 (2001)

    MATH  Google Scholar 

  14. Jürgensen, H., Konstantinidis, S.: Variable-length codes for error correction. In: Fülöp, Z. (ed.) ICALP 1995. LNCS, vol. 944, pp. 581–592. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  15. Jürgensen, H., Konstantinidis, S.: Error correction for channels with substitutions, insertions, and deletions. In: Chouinard, J.-Y., Fortier, P., Gulliver, T.A. (eds.) Information Theory 1995. LNCS, vol. 1133, pp. 149–163. Springer, Heidelberg (1996)

    Google Scholar 

  16. Jürgensen, H., Konstantinidis, S.: Codes. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 511–607. Springer, Berlin (1997)

    Chapter  Google Scholar 

  17. Jürgensen, H., Staiger, L.: Fault-tolerant acceptors for solid codes. In: Proceedings of the 14th Journées Montoises of Theoretical Computer Science, Universite ́ catho-lique de Louvain, Belgium, Louvain-la-Neuve, September 11-14, p. 8 (2012); the proceedings were distributed electronically on a memory stick at the conference

    Google Scholar 

  18. Jürgensen, H., Staiger, L.: Automata for solid codes. Manuscript in Preparation (2013)

    Google Scholar 

  19. Jürgensen, H., Yu, S.S.: Solid codes. J. Inform. Process. Cybernet., EIK 26, 563–574 (1990)

    MATH  Google Scholar 

  20. Konstantinidis, S.: Error Correction and Decodability. PhD Thesis, The University of Western Ontario, London, Canada (1996)

    Google Scholar 

  21. Konstantinidis, S.: Structural analysis of error-correcting codes for discrete channels that involve combinations of three basic error types. IEEE Trans. Inform. Theory 45(1), 60–77 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Konstantinidis, S.: An algebra of discrete channels that involve combinations of three basic error types. Inform. and Comput. 167, 120–131 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Konstantinidis, S.: Relationships between different error-correcting capabilities of a code. IEEE Trans. Inform. Theory 47(5), 2065–2069 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Konstantinidis, S.: Transducers and the properties of error-detection, error-correction, and finite-delay decodability. J. UCS 8(2), 278–291 (2002)

    MathSciNet  MATH  Google Scholar 

  25. Konstantinidis, S., O’Hearn, A.: Error-detecting properties of languages. Theoret. Comput. Sci. 276, 355–375 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Konstantinidis, S., Perron, S., Wilcox-O’Hearn, L.A.: On a simple method for detecting sychronization errors in coded messages. IEEE Trans. Inform. Theory 49(5), 1355–1363 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  27. Konstantinidis, S., Santean, N.: On the definition of stochastic λ-transducers. Internat. J. Comput. Math. 86(8), 1300–1310 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Konstantinidis, S., Silva, P.: Maximal error-detecting capabilities of formal languages. J. of Automata, Languages and Combinatorics 13(1), 55–71 (2008)

    MathSciNet  MATH  Google Scholar 

  29. Konstantinidis, S., Silva, P.V.: Computing maximal error-detecting capabilities and distances of regular languages. Fund. Inform. 101, 257–270 (2010)

    MathSciNet  MATH  Google Scholar 

  30. Levenshtein, V.I.: Self-adaptive automata for decoding messages (in Russian). Dokl. Akad. Nauk. SSSR 141, 1320–1323 (1961); Self-adaptive automata for decoding messages. Soviet Physics Dokl. 6, 1042–1045 (1962)

    Google Scholar 

  31. Levenshtein, V.I.: The inversion of finite automata (in Russian). Dokl. Akad. Nauk. SSSR 147, 1300–1303 (1962); The inversion of finite automata. Soviet Physics Dokl. 7, 1081–1084 (1963)

    Google Scholar 

  32. Levenshtein, V.I.: Decoding Automata, Invariant with Respect to the Initial State (in Russian). Problemy Kibernet. 12, 125–136 (1964)

    Google Scholar 

  33. Levenshtein, V.I.: Some Properties of Coding and Self-Adjusting Automata for Decoding Messages (in Russian). Problemy Kibernet. 11, 63–121 (1964); German translation: Über einige Eigenschaften von Codierungen und von selbstkorrigierenden Automaten zur Decodierung von Nachrichten. Probleme der Kybernetik 7, 96–163 (1966); An English translation is available from the Clearinghouse for Federal Scientific and Technical Information, U. S. Department of Commerce, under the title Some Properties of Coding and Self-Adjusting Automata for Decoding Messages, Problems of Cybernetics, Part II, document AD 667 849; it was prepared as document FTD-MT-24-126-67 by the Foreign Technology Division, U. S. Air Force

    Google Scholar 

  34. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals (in Russian). Dokl. Akad. Nauk. SSSR 163(4), 845–848 (1965); Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Dokl. 10, 707–710 (1966)

    Google Scholar 

  35. MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms, 6th edn. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  36. MacWilliams, F.J., Sloane, N.J.A.: The Theory of Error-Correcting Codes, vol. 2. North-Holland, Amsterdam (1977)

    MATH  Google Scholar 

  37. Mansour, M.F., Tewfik, A.H.: Convolutional decoding in the presence of synchronization errors. IEEE J. Selected Areas in Communications 28(2), 218–227 (2010)

    Article  Google Scholar 

  38. Markov, AI.A.: Non-recurrent coding. Problemy Kibernet. 8, 169–186 (1961) (in Russian); German translation: Nicht rekurrente Codierung. Probleme der Kybernetik 8, 154–175 (1962)

    Google Scholar 

  39. Maxted, J.C., Robinson, J.P.: Error recovery for variable length codes. IEEE Trans. Inform. Theory 31(6), 794–801 (1985)

    Article  MathSciNet  Google Scholar 

  40. Peterson, W.W., Weldon Jr., E.J.: Error-Correcting Codes, 2nd edn. MIT Press, Cambridge (1972)

    MATH  Google Scholar 

  41. Petrich, M., Thierrin, G.: The syntactic monoid of an infix code. Proc. Amer. Math. Soc. 109, 865–873 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  42. Pless, V.S., Huffman, W.C. (eds.): Handbook of Coding Theory, vol. 2. North-Holland, Elsevier (1998)

    MATH  Google Scholar 

  43. Romanov, O.T.: Invariant Decoding Automata without Look-ahead (in Russian). Problemy Kibernet. 17, 233–236 (1966)

    MATH  Google Scholar 

  44. Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, Cambridge (2009); English translation of Éléments de théorie des automates, Vuibert Informatique, Paris (2003)

    Google Scholar 

  45. Shyr, H.J.: Free Monoids and Languages, 3rd edn. Hon Min Book Company, Taichung (2001)

    Google Scholar 

  46. Starke, P.H.: Abstrakte Automaten. VEB Deutscher Verlag der Wissenschaften, Berlin (1969); English translation by I. Shepherd: Abstract Automata. North-Holland, Amsterdam (1972)

    Google Scholar 

  47. Thierrin, G.: Hypercodes, right convex languages and their syntactic monoids. Proc. Amer. Math. Soc. 83(2), 255–258 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  48. Thierrin, G.: The syntactic monoid of a hypercode. Semigroup Forum 6, 227–231 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  49. Valkema, E.: Syntaktische Monoide und Hypercodes. Semigroup Forum 13(77), 119–126 (1976/1977)

    Article  MathSciNet  Google Scholar 

  50. Yu, S.-S.: Languages and Codes. Tsang Hai Book Publishing Co., Taichung (2005)

    Google Scholar 

  51. Zigangirov, K.Sh.: Sequential decoding for a binary channel with drop-outs and insertions (in Russian). Problemy Peredachi Informatsii 5(2), 23–30 (1969); Sequential decoding for a binary channel with drop-outs and insertions. Problems Inform. Transmission 5(2), 17–22 (1969)

    Google Scholar 

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Authors and Affiliations

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

    Helmut Jürgensen

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  1. Helmut Jürgensen
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Editors and Affiliations

  1. Department of Mathematics and Computing Science, Saint Mary’s University, 923 Robie Street, NS B3H 3C3, Halifax, Canada

    Stavros Konstantinidis

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Jürgensen, H. (2013). Automata for Codes. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-39274-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39273-3

  • Online ISBN: 978-3-642-39274-0

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