Abstract
We consider the following decision problem: “Is a rational ω-language generated by a code ?” Since 1994, the codes admit a in terms of infinite words. We derive from this result the definition of a new class of languages, the reduced languages. A code is a reduced language but the converse does not hold. The idea is to “reduce” easy-to-obtain minimal ω-generators in order to obtain codes as ω-generators.
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References
Augros, X.: Etude des générateurs de langages de mots infinis. Master’s thesis, Univ. de Nice - Sophia Antipolis (june 1997)
Berstel, J., Perrin, D.: Theory of codes. Academic Press, London (1985)
Boasson, L., Nivat, M.: Adherences of languages. Journal of Computer and System Sciences 20, 285–309 (1980)
Büchi, J.R.: On a decision method in restricted second order arithmetics. In: International Congress on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1960)
Devolder, J.: Generators with bounded deciphering delay for rational ω-languages. Journal of Automata, Languages and Combinatorics 4(3), 183–204 (1999)
Devolder, J., Latteux, M., Litovsky, I., Staiger, L.: Codes and infinite words. Acta. Cybernetica 11(4), 241–256 (1994)
Julia, S.: Sur les codes et les ω-codes générateurs de langages de mots infinis. PhD thesis, Université de Nice - Sophia Antipolis (1996)
Julia, S.: A characteristic language for rational ω-powers. In: Proc. 3rd Int. Conf. Developments in Language Theory, pp. 299–308, Thessaloniki (1997)
Julia, S., Litovsky, I., Patrou, B.: On codes, ω-codes and ω-generators. Information Processing Letters 60(1), 1–5 (1996)
Karhumäki, J.: On three-element codes. Theoret. Comput. Sc. 40, 3–11 (1985)
Latteux, M., Timmerman, E.: Finitely generated ω-langages. Information Processing Letters 23, 171–175 (1986)
Litovsky, I.: Free submonoids and minimal ω-generators of R ω. Acta. Cybernetica 10(1-2), 35–43 (1991)
Litovsky, I.: Prefix-free languages as ω-generators. Information Processing Letters 37, 61–65 (1991)
Litovsky, I., Timmerman, E.: On generators of rational ω-power languages. Theoretical Computer Science 53, 187–200 (1987)
Lothaire, M.: Algebraic Combinatorics on Words. Cambridge (2002)
Perrin, D., Pin, J.E.: Infinite words. Elsevier Academic Press, Amsterdam (2004)
Staiger, L.: On infinitary finite length codes. Theoretical Informatics and Applications 20(4), 483–494 (1986)
Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, ch. 4, Elsevier Science Publishers, Amsterdam (1990)
Tran Vinh Duc. A la recherche des codes générateurs de langages de mots infinis. Master’s thesis, IFI Hanoï - Univ. de Nice - Sophia Antipolis (2006)
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Julia, S., Duc, T.V. (2007). Reduced Languages as ω-Generators. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_26
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DOI: https://doi.org/10.1007/978-3-540-73208-2_26
Publisher Name: Springer, Berlin, Heidelberg
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