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Bond-free DNA language classes

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Abstract

The absence of the ability to form a specified set of bonds in a collection of DNA strands is crucial in the design of experiments encoding algorithmic problems as single- or double-stranded DNA. Recently, the specification of the bonding types to be avoided has been formalized by defining bond-free properties. Bond-free properties generalize several bonding properties which have been studied in the context of DNA computing. In this paper, we consider a bond-free property as defining a class of languages. We study the properties of these classes of languages. We develop new unary operators on languages for characterizing bond-free properties exactly, using familiar code-theoretic equations. These new operators provide a new characterization of maximal bond-free properties as well. We also focus on relationships to classes of languages from the theory of codes.

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References

  • Adleman L (1994) Molecular computation of solutions to combinatorial problems. Science 266:1021–1024

    Article  Google Scholar 

  • Berstel J and Perrin D (1996) Theory of Codes. Available at http://www-igm.univ-mlv.fr/%7Eberstel/LivreCodes/Codes.html

  • Domaratzki M (2004a) Deletion along trajectories. Theoretical Computer Science 320(2–3):293–313

    Article  MATH  MathSciNet  Google Scholar 

  • Domaratzki M (2004b) Trajectory-Based Codes. Acta Informatica 40(6–7):491–527

    Article  MATH  MathSciNet  Google Scholar 

  • Domaratzki M (2004c) Trajectory-Based Embedding Relations. Fundamenta Informatica 59(4):349–363

    MATH  MathSciNet  Google Scholar 

  • Domaratzki M (2005) More Words on Trajectories. Bulletin of the European Association of Theoretical Computer Science 86:107–145

    MathSciNet  Google Scholar 

  • Domaratzki M and Salomaa K (2005) Codes defined by multiple sets of trajectories. In: Esik Z and Fulop Z (eds) Automata and Formal Languages (AFL’05), pp. 97–111, Theoretical Computer Science (to appear)

  • Ginsburg S (1966) The Mathematical Theory of Context-Free Languages. McGraw-Hill

  • Hopcroft JE and Ullman JD (1979) Introduction to Automata Theory, Languages, and Computation. Addison-Wesley

  • Hunt H, Rosenkrantz D (1977) On equivalence and containment problems for formal languages. Journal of the Association for Computing Machinery 24(3):387–396

    MATH  MathSciNet  Google Scholar 

  • Hussini S, Kari L, Konstantinidis S (2002) Coding properties of DNA languages. Theoretical Computer Science 290(3):1557–1579

    Article  MathSciNet  Google Scholar 

  • Jürgensen H and Konstantinidis S (1997) Codes. In: Rozenberg G and Salomaa A (eds) Handbook of Formal Languages, Springer pp. 511–600

  • Kadrie A, Dare V, Thomas D, Subramanian K (2001) Algebraic Properties of the shuffle over ω-trajectories. Information Processing Letters 80(3):139–144

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Kitto R and Thierrin G (2003a) Codes, involutions and DNA encoding. In: Brauer W et al. (eds) Vol. 2300 of LNCS, pp. 376–393

  • Kari L and Sosík P (2003) Language deletions on trajectories. Technical Report 606, Computer Science Department, University of Western Ontario

  • Kari L, Sosík P (2005) Aspects of shuffle and deletion on trajectories. Theoretical Computer Science 332(1–3):47–61

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Konstantinidis S (2005) Language equations, maximality and error-detection. Journal of Computer and System Sciences 70:157–178

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Konstantinidis S, Losseva E, Wozniak G (2003b) Sticky-free and overhang-free DNA languages. Acta Informatica 40:119–157

    Article  MATH  MathSciNet  Google Scholar 

  • Kari L, Konstantinidis S, Sosík P (2005a) Bond-free Languages: Formalisms, Maximality and Construction Methods. International Journal of Foundations of Computer Sciences 16:1039–1070

    Article  MATH  Google Scholar 

  • Kari L, Konstantinidis S, Sosík P (2005b) On properties of bond-free DNA languages. Theoretical Computer Science 334:131–159

    Article  MATH  Google Scholar 

  • Mateescu A, Rozenberg G, Salomaa A (1998) Shuffle on trajectories: Syntactic constraints. Theoretical Computer Science 197:1–56

    Article  MATH  MathSciNet  Google Scholar 

  • Nowotka D and Harju T (2004) Periodicity and unbordered words. In: Diekert V and Habib M (eds) STACS (Montpellier, 2004), Vol. 2996 of LNCS, pp. 294–304

  • Shyr H (2001) Free Monoids and Languages. Hon Min Book Company, Taichung, Taiwan

    Google Scholar 

  • Yu S (1997) Regular languages. In: Rozenberg G and Salomaa A (eds) Handbook of Formal Languages, Springer pp. 41–110.

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Acknowledgements

Many thanks to the anonymous referees for their suggestions which improved the presentation of this article.

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Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, Winnipeg, MB, R3T 2T2, Canada

    Michael Domaratzki

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  1. Michael Domaratzki
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Correspondence to Michael Domaratzki.

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Research supported in part by a grant from NSERC.

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Domaratzki, M. Bond-free DNA language classes. Nat Comput 6, 371–402 (2007). https://doi.org/10.1007/s11047-006-9022-8

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  • DOI: https://doi.org/10.1007/s11047-006-9022-8

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