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. © 2011 Springer-Verlag.
CITATION STYLE
Rodaro, E., & Silva, P. V. (2011). Never minimal automata and the rainbow bipartite subgraph problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6795 LNCS, pp. 374–385). https://doi.org/10.1007/978-3-642-22321-1_32
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