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Never Minimal Automata and the Rainbow Bipartite Subgraph Problem

  • Emanuele Rodaro
  • Pedro V. Silva
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)

Abstract

Never minimal automata, introduced in [4], are strongly connected automata which are not minimal for any choice of their final states. In [4] the authors raise the question whether recognizing such automata is a polynomial time task or not. In this paper, we show that the complement of this problem is equivalent to the problem of checking whether or not in an edge-colored graph there is a bipartite subgraph whose edges are colored using all the colors. We prove that this graph theoretic problem is NP-complete, showing that checking the property of never-minimality is unlikely a polynomial time task.

Keywords

Equivalence Relation Colored Graph Truth Assignment Bipartite Subgraph Orthogonal Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Goralcik, P., Koubek, V.: On the disjunctive set problem. Theoretical Computer Science 204, 99–118 (1998)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Kano, M., Li, X.: Monochromatic and heterochromatic subgraphs in edge-colored graphs-a survey. Graphs and Combinatorics 24, 237–263 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley Longman, Amsterdam (1995)MATHGoogle Scholar
  4. 4.
    Restivo, A., Vaglica, R.: Automata with extremal minimality conditions. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 399–410. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Emanuele Rodaro
    • 1
  • Pedro V. Silva
    • 1
  1. 1.Departamento de Matemática, Faculdade de CiênciasUniversidade do PortoPortoPortugal

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