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Insertion-Deletion Systems over Relational Words

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Reachability Problems (RP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9899))

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Abstract

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with two binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable reachability problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidability of reachability questions.

I. Potapov — The author was partially supported by EPSRC grant (EP/M00077X/1)

O. Prianychnykova — Supported by the DFG-Project “Speichermechanismen als Monoide”, KU 1107/9-1.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Igor Potapov

  2. Technische Universität Ilmenau, Ilmenau, Germany

    Olena Prianychnykova

  3. LACL, Departement Informatique, Université Paris Est Créteil, Créteil, France

    Sergey Verlan

Authors
  1. Igor Potapov
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  2. Olena Prianychnykova
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  3. Sergey Verlan
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Corresponding author

Correspondence to Olena Prianychnykova .

Editor information

Editors and Affiliations

  1. Aalborg University, Aalborg, Denmark

    Kim Guldstrand Larsen

  2. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

  3. Aalborg University, Aalborg, Denmark

    Jiří Srba

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Potapov, I., Prianychnykova, O., Verlan, S. (2016). Insertion-Deletion Systems over Relational Words. In: Larsen, K., Potapov, I., Srba, J. (eds) Reachability Problems. RP 2016. Lecture Notes in Computer Science(), vol 9899. Springer, Cham. https://doi.org/10.1007/978-3-319-45994-3_13

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  • DOI: https://doi.org/10.1007/978-3-319-45994-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45993-6

  • Online ISBN: 978-3-319-45994-3

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