Insertion-Deletion Systems over Relational Words

  • Igor Potapov
  • Olena PrianychnykovaEmail author
  • Sergey Verlan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9899)


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.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Igor Potapov
    • 1
  • Olena Prianychnykova
    • 2
    Email author
  • Sergey Verlan
    • 3
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.Technische Universität IlmenauIlmenauGermany
  3. 3.LACL, Departement InformatiqueUniversité Paris Est CréteilCréteilFrance

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