Skip to main content
Springer Nature Link
Log in

Decision Problems for Linear and Circular Splicing Systems

  • Conference paper
  • First Online:
Developments in Language Theory (DLT 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2450))

Included in the following conference series:

  • 355 Accesses

Abstract

We will consider here the splicing systems, generative devices inspired by cut and paste phenomena on DNA molecules under the action of restriction and ligase enzymes. A DNA strand can be viewed as a string over a four letter alphabet (the four deoxyribonucleotides), therefore we can model DNA computation within the framework of formal language theory. In spite of a vast literature on splicing systems, briefly surveyed here, a few problems related to their computational power are still open. We intend to evidence how classical techniques and concepts in automata theory are a legitimate tool for investigating some of these problems.

Partially supported by MIUR Project “Linguaggi Formali e Automi: teoria ed applicazioni” and by the contribution of EU Commission under The Fifth Framework Programme, project MolCoNet IST-2001-32008.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adleman, L. M.: Molecular computation of solutions to combinatorial problems. Science 226 (1994) 1021–1024

    Article  Google Scholar 

  2. Berstel, J., Perrin, D.: Theory of codes. Academic Press, New York (1985)

    MATH  Google Scholar 

  3. Berstel, J., Restivo, A.: Codes et sousmonoides fermes par conjugaison. Sem. LITP 81–45 (1981) 10 pages

    Google Scholar 

  4. Bonizzoni, P., De Felice, C., Mauri, G., Zizza, R.: DNA and circular splicing. In: Condon, A., Rozenberg, G. (eds.): DNA Computing. Lecture Notes in Computer Science, Vol. 2054. Springer-Verlag, New York (2001) 117–129

    Chapter  Google Scholar 

  5. Bonizzoni, P., De Felice, C., Mauri, G., Zizza, R.: Circular splicing and regularity (2002) submitted

    Google Scholar 

  6. Bonizzoni, P., De Felice, C., Mauri, G., Zizza, R.: On the power of linear and circular splicing (2002) submitted

    Google Scholar 

  7. Bonizzoni, P., De Felice, C., Mauri, G., Zizza, R.: The structure of regular reflexive splicing languages via Schützenberger constants (2002) manuscript

    Google Scholar 

  8. Bonizzoni, P., Ferretti, C., Mauri, G.: Splicing systems with marked rules. Romanian Journal of Information Science and Technology 1:4 (1998) 295–306

    Google Scholar 

  9. Bonizzoni, P., Ferretti, C., Mauri, G., Zizza, R.: Separating some splicing models. Information Processing Letters 76:6 (2001) 255–259

    Article  MathSciNet  Google Scholar 

  10. Choffrut, C., Karhumaki, J.: Combinatorics onWords. In: Rozenberg, G., Salomaa, A., (eds.): Handbook of Formal Languages, Vol. 1. Springer-Verlag, (1996) 329–438

    Google Scholar 

  11. Culik, K., Harju, T.: Splicing semigroups of dominoes and DNA. Discrete Applied Mathematics 31 (1991) 261–277

    Article  MATH  MathSciNet  Google Scholar 

  12. De Luca, A., Restivo, A.: A characterization of strictly locally testable languages and its application to subsemigroups. Information and Control 44 (1980) 300–319

    Article  MATH  MathSciNet  Google Scholar 

  13. Denningho., K.L., Gatterdam, R.W.: On the undecidability of splicing systems. International Journal of Computer Math. 27 (1989) 133–145

    Article  Google Scholar 

  14. Freund, R., Kari, L., Paun, Gh.: DNA Computing based on splicing. The existence of universal computers. Theory of Computing Systems 32 (1999) 69–112

    Article  MATH  MathSciNet  Google Scholar 

  15. Gatterdam, R.W.: Algorithms for splicing systems. SIAM Journal of Computing21:3 (1992) 507–520

    Article  MATH  MathSciNet  Google Scholar 

  16. Goode, E., Head, T., Pixton D.: private communication

    Google Scholar 

  17. Goode, E., Pixton, D.: Semi-simple splicing systems. In: Martin-Vide, C., Mitrana, V. (eds.): Where Mathematics, Computer Science, Linguistics and Biology Meet. Kluwer Academic Publ., Dordrecht (2001) 343–357

    Google Scholar 

  18. Head, T.: Splicing schemes and DNA. In: Lindenmayer Systems. Impacts on Theoretical Computer Science and Developmental Biology. Springer-Verlag, Berlin (1992) 371–383

    Google Scholar 

  19. Head, T.: Formal Language Theory and DNA. An analysis of the generative capacity of specific recombinant behaviours. Bull. Math. Biol. 49 (1987) 737–759

    MATH  MathSciNet  Google Scholar 

  20. Head, T.: Splicing languages generated with one sided context. In: Paun, Gh. (ed.): Computing with Bio-molecules. Theory and Experiments, Springer-Verlag Singapore (1998)

    Google Scholar 

  21. Head, T.: Splicing representations of strictly locally testable languages. Discrete Applied Math. 87 (1998) 139–147

    Article  MATH  MathSciNet  Google Scholar 

  22. Head, T.: Circular suggestions for DNA Computing. In: Carbone, A., Gromov, M., Pruzinkiewicz, P. (eds.): Pattern Formation in Biology, Vision and Dynamics. World Scientific, Singapore and London, to appear

    Google Scholar 

  23. Head, T.: Splicing systems. Regular languages and below. In: Pre-Proc. of DNA8 (2002)

    Google Scholar 

  24. Head, T., Paun, Gh., Pixton, D.: Language theory and molecular genetics. Generative mechanisms suggested by DNA recombination. In: Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, Vol. 2. Springer-Verlag (1996) 295–360

    Google Scholar 

  25. Head, T., Rozenberg, G., Bladergroen, R., Breek, C., Lommerse, P., Spaink, H.: Computing with DNA by operating on plasmids. BioSystems 57 (2000) 87–93

    Article  Google Scholar 

  26. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. 2nd edn. Addison-Wesley, Reading, Mass. (2001)

    MATH  Google Scholar 

  27. Jonoska, N., Karl, S.: A molecular computation of the road coloring problem. In: Proc. of 2nd Annual Meeting on DNA Based Computers. DIMACS Workshop (1996) 148–158

    Google Scholar 

  28. Kari, L.: DNA computing. An arrival of biological mathematics. The Mathematical Intelligence 19:2 (1999) 9–22

    MathSciNet  Google Scholar 

  29. Kim, S.M.: An Algorithm for Identifying Spliced Languages. In: Proc. of Cocoon97. Lecture Notes in Computer Science, Vol. 1276. Springer-Verlag (1997) 403–411

    Google Scholar 

  30. Kim, S.M.: Computational modeling for genetic splicing systems. SIAM Journal of Computing 26 (1997) 1284–1309

    Article  MATH  Google Scholar 

  31. Lothaire, M.: Combinatorics on Words. Encyclopedia of Math. and its Applications. Addison Wesley Publishing Company (1983)

    Google Scholar 

  32. McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge, Mass. (1971)

    Google Scholar 

  33. Mateescu, A., Paun, Gh., Rozenberg, G., Salomaa, A.: Simple splicing systems. Discrete Applied Mathematics 84 (1998) 145–163

    Article  MATH  MathSciNet  Google Scholar 

  34. Paun, Gh.: On the splicing operation. Discrete Applied Mathematics 70 (1996) 57–79

    Article  MATH  MathSciNet  Google Scholar 

  35. Paun, Gh.: Regular extended H systems are computationally universal. Journal of Automata, Languages and Combinatorics. 1:1 (1996) 27–36

    MATH  MathSciNet  Google Scholar 

  36. Paun, Gh., Salomaa, A.: DNA computing based on the splicing operation. Mathematica Japonica 43:3 (1996) 607–632

    MATH  MathSciNet  Google Scholar 

  37. Paun, Gh., Rozenberg, G., Salomaa, A.: Computing by splicing. Theoretical Computer Science 168:2 (1996) 321–336

    Article  MATH  MathSciNet  Google Scholar 

  38. Paun, Gh., Rozenberg, G., Salomaa, A.: DNA computing, New Computing Paradigms. Springer-Verlag (1998)

    Google Scholar 

  39. Perrin, D.: Finite Automata. In: van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science, Vol. B. Elsevier (1990) 1–57

    Google Scholar 

  40. Pixton, D.: Splicing in abstract families of languages. Theoretical Computer Science 234 (2000) 135–166

    Article  MATH  MathSciNet  Google Scholar 

  41. Pixton, D.: Linear and Circular Splicing Systems. In: Proc. of 1st Int. Symp. on Int. in Neural and Biological Systems (1996) 181–188

    Google Scholar 

  42. Pixton, D.: Regularity of splicing languages. Discrete Applied Mathematics 69 (1996) 101–124

    Article  MATH  MathSciNet  Google Scholar 

  43. Reis, C., Thierren, G.: Reflective star languages and codes. Information and Control 42 (1979) 1–9

    Article  MATH  MathSciNet  Google Scholar 

  44. Schützenberger, M.-P.: Sur certaines opérations de fermeture dans le langages rationnels. Symposia Mathematica 15 (1975) 245–253

    Google Scholar 

  45. Siromoney, R.: Distributed Circular Systems. In: Pre-Proc. of Grammar Systems 2000, Austria

    Google Scholar 

  46. Siromoney, R., Subramanian, K.G., Dare, A.: Circular DNA and Splicing Systems. In: Proc. of ICPIA. Lecture Notes in Computer Science, Vol. 654. Springer-Verlag (1992) 260–273

    Google Scholar 

  47. Yokomori, T., Kobayaski, S., Ferretti, C.: On the power of circular splicing systems and DNA computability. In: Proc. of IEEE Int. Conf. Evol. Comp. ICEC99

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica Sistemistica e Comunicazione, Università degli Studi di Milano - Bicocca, Via Bicocca degli Arcimboldi 8, 20126, Milano, Italy

    Paola Bonizzoni & Giancarlo Mauri

  2. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi, SA, Italy

    Clelia De Felice & Rosalba Zizza

Authors
  1. Paola Bonizzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Clelia De Felice
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giancarlo Mauri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rosalba Zizza
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Science and Faculty of Engineering, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Masami Ito  & Masafumi Toyama  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bonizzoni, P., De Felice, C., Mauri, G., Zizza, R. (2003). Decision Problems for Linear and Circular Splicing Systems. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2002. Lecture Notes in Computer Science, vol 2450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45005-X_7

Download citation

  • DOI: https://doi.org/10.1007/3-540-45005-X_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40431-6

  • Online ISBN: 978-3-540-45005-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics