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Infinite Strings Generated by Insertions

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Abstract

The process of generation of strings over a finite alphabet by inserting characters at an arbitrary place in the string is considered. A topology on the set of strings is introduced, in which closed sets are defined to be sets of strings that are invariant with respect to the insertion of characters. An infinite insertion string is defined to be a set of infinite sequences of insertions ending in the same open sets. The number of infinite insertion strings is proved to be countable. It is proved also that there is a relationship between the countability of the completion of partially well-ordered sets by infinite elements and the fulfillment of an analogue of Dickson's and Higman's lemmas for them.

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REFERENCES

  1. Goldfarb, L., Golubitsky, O., and Korkin, D., What Is a Structural Representation? Techn. Report TR00-137, Faculty Comput. Sci., U.N.B., 2001.

  2. Golubitsky, O., On the Generating Process and the Class Typicality Measure, Techn. Report TR02-151, Faculty Comput. Sci., U.N.B., 2002.

  3. Dershowitz, N. and Jouannaud, J.-P., Rewrite Systems, Handbook of Theoretical Computer Science, van Leeuwen, J., Ed., Amsterdam: North-Holland, 1990, vol. B, ch. 6, pp.243-320.

    Google Scholar 

  4. Cox, D., Little, J., and O'Shea, D., Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, New York: Springer, 1998. Translated under the title Idealy, mnogoobraziya i algoritmy, Moscow: Mir, 2000.

    Google Scholar 

  5. Higman, G., Ordering by Divisibility in Abstract Algebras, Proc. London Math. Soc., 1952, vol. 2,no. 7, pp. 326–336.

    Google Scholar 

  6. Murthy, C. and Russell, J.R., A Constructive Proof of Higman's Lemma, LICS, 1990, pp. 257–267.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Vorob'evy gory, Moscow, 119992, Russia

    O. D. Golubitsky

  2. Faculty of Computer Science, University of New Brunswick, 540 Windsor St., Fredericton, E3B5A3, Canada

    S. Falconer

Authors
  1. O. D. Golubitsky
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  2. S. Falconer
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Golubitsky, O.D., Falconer, S. Infinite Strings Generated by Insertions. Programming and Computer Software 30, 110–114 (2004). https://doi.org/10.1023/B:PACS.0000021270.99375.f5

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  • DOI: https://doi.org/10.1023/B:PACS.0000021270.99375.f5

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