Consensus String Problem for Multiple Regular Languages

  • Yo-Sub Han
  • Sang-Ki KoEmail author
  • Timothy Ng
  • Kai Salomaa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10168)


The consensus string (or center string, closest string) of a set S of strings is defined as a string which is within a radius r from all strings in S. It is well-known that the consensus string problem for a finite set of equal-length strings is NP-complete. We study the consensus string problem for multiple regular languages. We define the consensus string of languages \(L_1, \ldots , L_k\) to be within distance at most r to some string in each of the languages \(L_1, \ldots , L_k\). We also study the complexity of some parameterized variants of the consensus string problem. For a constant k, we give a polynomial time algorithm for the consensus string problem for k regular languages using additive weighted finite automata. We show that the consensus string problem for multiple regular languages becomes intractable when k is not fixed. We also examine the case when the length of the consensus string is given as part of input.


Consensus string problem Computational complexity Regular languages Edit-distance 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Yo-Sub Han
    • 1
  • Sang-Ki Ko
    • 2
    Email author
  • Timothy Ng
    • 3
  • Kai Salomaa
    • 3
  1. 1.Department of Computer ScienceYonsei UniversitySeoulRepublic of Korea
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  3. 3.School of ComputingQueen’s UniversityKingstonCanada

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