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)


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.


Equivalence Relation Colored Graph Truth Assignment Bipartite Subgraph Orthogonal Family 
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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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