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Splicing Systems: Regularity and Below

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Book cover DNA Computing (DNA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2568))

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Abstract

The motivation for the development of splicing theory is recalled. A ttention is restricted to finite splicing systems, which are those having only finitely many rules and finitely many initial strings.Languages generated by such systems are necessarily regular, but not all regular languages can be so generated.Th e splicing systems that arose originally, as models of enzymatic actions, have two special properties called reflexivity and symmetry.We announce the Pixton-Goode procedure for deciding whether a given regular language can be generated by a finite reflexive splicing system.A lthough the correctness of the algorithm is not demonstrated here, two propositions that serve as major tools in the demonstration are stated.One of these is a powerful pumping lemma.Th e concept of the syntactic monoid of a language provides sharp conceptual clarity in this area.We believe that there may be yet unrealized results to be found that interweave splicing theory with subclasses of the class of regular languages and we invite others to join in these investigations.

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References

  1. L. Adleman, Molecular computation of solutions of combinatorial problems, Science 266(1994)1021–1024.

    Article  Google Scholar 

  2. J. Almeida, Finite Semigroups and Universal Algebra, World Scientific, Singapore (1994).

    Google Scholar 

  3. P. Bonizzoni, C. De Felice, G.M auri, R. Zizza, On the power of linear and circular splicing systems, (submitted).

    Google Scholar 

  4. P. Bonizzoni, C. De Felice, G. Mauri, R. Zizza, Decision problems for linear and circular splicing, DLT2002 volume of LNCS (to appear).

    Google Scholar 

  5. P. Bonizzoni, C. De Felice, G. Mauri, R. Zizza, The structure of reflexive splicing languages via Schutzenberger constants, (submitted).

    Google Scholar 

  6. K. Culik II, T. Harju, The regularity of splicing systems and DNA, in: Proc. ICALP’ 89, LCNS 372(1989)222–233.

    Google Scholar 

  7. K. Culik II, T. Harju, Splicing semigroups of dominoes and DNA, Discrete Appl. Math. 31(1991)261–277.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. DeLuca, A. Restivo, A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup, Inform. and Control 44(1980)300–319.

    Article  MATH  MathSciNet  Google Scholar 

  9. K.L. Denningffho., R. Gatterdam, On the undecidability of splicing systems, Inter. J. Computer Math. 27(1989)133–145.

    Article  Google Scholar 

  10. R.W. Gatterdam, Splicing systems and regularity, Inter. J. Computer Math. 31(1989)63–67.

    Article  MATH  Google Scholar 

  11. T. E. Goode Laun, Constants and Splicing Systems, Dissertation Binghamton University, Binghamton, New York(1999).

    Google Scholar 

  12. T. Head, Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors, Bull. Math. Biology 49(1987)737–759.

    MATH  MathSciNet  Google Scholar 

  13. T. Head, Splicing representations of strictly locally testable languages, Discrete Appl. Math. 87(1990)139–147.

    Article  MathSciNet  Google Scholar 

  14. T. Head, Splicing languages with one-sided context, in: Gh. Paun, Ed., Biomolecular Computing — Theory and Experiment, Springer-Verlag (1998)269–282.

    Google Scholar 

  15. T.Head, Gh, Paun, D. Pixton, Language theory and molecular genetics: generative mechanisms suggested by DNA recombinations, Chapter 7, Vol.2 of: G. Rozenberg & A. Salomaa, Eds., Handbook of Formal Languages, Springer, Berlin (1997)295–360.

    Google Scholar 

  16. J. Kari, L. Kari, Context-free recombination, in: C. Martin-Vide & V. Mitrana, Eds., Where Mathematics, Computer Science, Linguistics and Biology Meet, Kluwer Academic Pub., Dordrecht (2001).

    Google Scholar 

  17. B. Lewin, Genes, (1st.ed.) Wiley, New York (1983).

    Google Scholar 

  18. A. Mateescu, Gh. Paun, G. Rozenberg, A. Salomaa, Simple splicing systems, Discrete Appl. Math. 84(1996)145–163.

    Article  MathSciNet  Google Scholar 

  19. R. McNaughton, S. Papert, Counter-free Automata, MIT Press, Cambridge, MA (1971).

    MATH  Google Scholar 

  20. Gh. Paun, G. Rozenberg, A. Salomaa, DNA Computing — New Computing Pardigms, Springer-Verlag, Berlin (1998).

    Google Scholar 

  21. J. E. Pin, Varieties of Formal Languages, Plenum Pub.Co. (1986).

    Google Scholar 

  22. D. Pixton, Regularity of splicing systems, Discrete Appl. Math. 69(1996)101–124.

    Article  MATH  MathSciNet  Google Scholar 

  23. H. Straubing, Finite Automata, Formal Logic, and Circuit Complexity, Birkhauser, Boston, MA (1994).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Binghamton University, Binghamton, New York, USA

    Tom Head & Dennis Pixton

  2. Mathematics Department, Towson State University, Towson, Maryland, USA

    Elizabeth Goode

Authors
  1. Tom Head
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  2. Dennis Pixton
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  3. Elizabeth Goode
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Toyko Graduate School of Information Science and Technology, 7-3-1 Hongo, Bunkyo-ku, 113-8565, Tokyo, Japan

    Masami Hagiya

  2. Division of Complex Systems Technology, Hokkaido University Graduate School of Engineering, N-13, W-8, KITA-KU, 060, Sapporo, Japan

    Azuma Ohuchi

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© 2003 Springer-Verlag Berlin Heidelberg

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Head, T., Pixton, D., Goode, E. (2003). Splicing Systems: Regularity and Below . In: Hagiya, M., Ohuchi, A. (eds) DNA Computing. DNA 2002. Lecture Notes in Computer Science, vol 2568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36440-4_23

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  • DOI: https://doi.org/10.1007/3-540-36440-4_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00531-5

  • Online ISBN: 978-3-540-36440-5

  • eBook Packages: Springer Book Archive

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