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Extended Watson–Crick L systems with regular trigger languages and restricted derivation modes

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Abstract

Watson–Crick Lindenmayer systems add a control mechanism to ordinary Lindenmayer (L) system derivations. The mechanism is inspired by the complementarity relation in DNA strings, and it is formally defined in terms of a trigger language (trigger, for short). It is known that Watson–Crick E0L systems employed with the standard trigger (which is a context-free language) are computationally universal. Here we show that all recursively enumerable languages can be generated already by a Uni-Transitional Watson–Crick E0L system with a regular trigger. A system is Uni-Transitional if any derivation of a terminal word can apply the Watson–Crick morphism at most once. We introduce a weak derivation mode where, for sentential forms in the trigger language, the derivation chooses nondeterministically whether or not to apply the Watson–Crick morphism. We show that Watson–Crick E0L systems employing a regular trigger and the weak derivation mode remain computationally universal but, on the other hand, the corresponding Uni-Transitional systems generate only a subclass of the ET0L languages. We consider also the computational power of Watson–Crick (deterministic) ET0L systems.

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References

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

    Article  Google Scholar 

  • Bar-Hillel Y, Perles M, Shamir E (1961) On formal properties of simple phrase-structure grammars. Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 14:143–177

    MathSciNet  MATH  Google Scholar 

  • Csima J, Csuhaj-Varjú E, Salomaa A (2003) Power and size of extended Watson–Crick L systems. Theor Comput Sci 290(3):1665–1678

    Article  MATH  Google Scholar 

  • Csuhaj-Varjú E (2000) Computing by networks of Watson–Crick D0L systems. In: Ito M (eds) Algebraic systems, formal languages and computation. RIMS Kokyroku 1166, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, pp 43–51

    Google Scholar 

  • Csuhaj-Varjú E (2004) Networks of standard Watson–Crick D0L systems with incomplete information communication. In: Karhumäki J, Maurer HA, Paun G, Rozenberg G (eds) Theory is forever, vol 3113 of Lecture notes in computer science, Springer, Berlin, pp 35–48

    Google Scholar 

  • Csuhaj-Varjú E, Salomaa A (2000) Networks of Watson–Crick D0L systems. In: Ito M, Imaoka T (eds) Words, languages & combinatorics III. Proceedings of the international colloquium, Kyoto, Japan, 2003. World Scientific Publishing Co., Singapore, pp 134–149

  • Culik II KC (1979) A purely homomorphic characterization of recursively enumerable sets. J ACM 26(2):345–350

    Google Scholar 

  • Honkala J, Salomaa A (2001) Watson–Crick D0L systems with regular triggers. Theor Comput Sci 259(1–2):689–698

    Article  MathSciNet  MATH  Google Scholar 

  • Mihalache V, Salomaa A (1997) Lindenmayer and DNA: Watson–Crick D0L systems. Bull EATCS 62:160–175

    Google Scholar 

  • Mihalache V, Salomaa A (2001) Language-theoretic aspects of DNA complementarity. Theor Comput Sci 250(1–2):163–178

    Article  MathSciNet  MATH  Google Scholar 

  • Penttonen M (1974) One-sided and two-sided context in formal grammars. Inf Control 25(4):371–392

    Article  MathSciNet  MATH  Google Scholar 

  • Rozenberg G, Salomaa A (1980) The mathematical theory of L systems. Academic Press, New York

    MATH  Google Scholar 

  • Rozenberg, G, Salomaa, A (eds) (1997) Handbook of formal languages, vol 1: word, language, grammar. Springer, New York

    MATH  Google Scholar 

  • Salomaa A (1997) Turing, Watson–Crick and Lindenmayer aspects of DNA complementarity. In: Calude C, Casti J, Dinneen MJ (eds) Unconventional models of computation. Springer, Singapore, pp 94–107

  • Salomaa A (1999) Watson–Crick walks and roads on D0L graphs. Acta Cybern 14(1):179–192

    MathSciNet  MATH  Google Scholar 

  • Salomaa A (2002) Uni-transitional Watson–Crick D0L systems. Theor Comput Sci 281(1–2):537–553

    Article  MathSciNet  MATH  Google Scholar 

  • Sears D (2010) The computational power of extended Watson–Crick L systems. Master’s thesis, School of Computing, Queen’s University, Kingston

  • Sosík P (2001) D0L system + Watson–Crick complementarity = universal computation. In: Margenstern M, Rogozhin Y (eds) MCU, vol 2055 of lecture notes in computer science, Springer, Berlin, pp 308–320

    Google Scholar 

  • Sosík P (2002) Universal computation with Watson–Crick D0L systems. Theor Comput Sci 289(1):485–501

    Article  MATH  Google Scholar 

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Correspondence to David Sears.

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Sears, D., Salomaa, K. Extended Watson–Crick L systems with regular trigger languages and restricted derivation modes. Nat Comput 11, 653–664 (2012). https://doi.org/10.1007/s11047-012-9329-6

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