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Universality of Graph-controlled Leftist Insertion-deletion Systems with Two States

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Book cover Machines, Computations, and Universality (MCU 2015)

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Abstract

In this article, we consider leftist insertion-deletion systems, in which all rules have contexts on the same side, and may only insert or delete one symbol at a time. We start by introducing extended rules, in which the contexts may be specified as regular expressions, instead of fixed words. We then prove that leftist systems with such extended rules and two-state graph control can simulate any arbitrary 2-tag system. Finally, we show how our construction can be simulated in its turn by graph-controlled leftist insertion-deletion systems with conventional rules of sizes (1, 1, 0; 1, 2, 0) and (1, 2, 0; 1, 1, 0) (where the first three numbers represent the maximal size of the inserted string and the maximal size of the left and right contexts respectively, while the last three numbers provide the same information about deletion rules), which implies that the latter systems are universal.

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Acknowledgments

The authors would like to acknowledge the support of ANR project SynBioTIC.

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Authors and Affiliations

  1. Laboratoire d’Algorithmique, Complexité et Logique, Université Paris Est – Créteil Val de Marne, 61, av. gén. de Gaulle, 94010, Créteil, France

    Sergiu Ivanov & Sergey Verlan

  2. Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Academiei 5, Chisinau, MD-2028, Moldova

    Sergey Verlan

Authors
  1. Sergiu Ivanov
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  2. Sergey Verlan
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Correspondence to Sergey Verlan .

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Editors and Affiliations

  1. Université d'Orléans, Orléans, France

    Jerome Durand-Lose

  2. Eastern Mediterranean University, Famagusta, Cyprus

    Benedek Nagy

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Ivanov, S., Verlan, S. (2015). Universality of Graph-controlled Leftist Insertion-deletion Systems with Two States. In: Durand-Lose, J., Nagy, B. (eds) Machines, Computations, and Universality. MCU 2015. Lecture Notes in Computer Science(), vol 9288. Springer, Cham. https://doi.org/10.1007/978-3-319-23111-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-23111-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23110-5

  • Online ISBN: 978-3-319-23111-2

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