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.
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Rodaro, E., Silva, P.V. (2011). Never Minimal Automata and the Rainbow Bipartite Subgraph Problem. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_32
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DOI: https://doi.org/10.1007/978-3-642-22321-1_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22320-4
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