On the Parameterised Complexity of String Morphism Problems

Authors Henning Fernau, Markus L. Schmid, Yngve Villanger

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Henning Fernau
Markus L. Schmid
Yngve Villanger

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Henning Fernau, Markus L. Schmid, and Yngve Villanger. On the Parameterised Complexity of String Morphism Problems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 55-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


Given a source string u and a target string w, to decide whether w can be obtained by applying a string morphism on u (i. e., uniformly replacing the symbols in u by strings) constitutes an NP-complete problem. For example, the target string w := baaba can be obtained from the source string u := aba, by replacing a and b in u by the strings ba and a, respectively. In this paper, we contribute to the recently started investigation of the computational complexity of the string morphism problem by studying it in the framework of parameterised complexity.
  • String Problems
  • String Morphisms
  • Parameterised Complexity
  • Exponential Time Hypothesis
  • Pattern Languages


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