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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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Authors and Affiliations

  1. School of Computing, Queen’s University, Kingston, ON, K7L 3N6, Canada

    David Sears & Kai Salomaa

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  1. David Sears
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  2. Kai Salomaa
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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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  • DOI: https://doi.org/10.1007/s11047-012-9329-6

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