Consensus String Problem for Multiple Regular Languages

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
  • 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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