On the disjunctive set problem
Theoretical Computer Science - Special issue: papers dedicated to the memory of Marcel-Paul Schützenberger
Monochromatic and Heterochromatic Subgraphs in Edge-Colored Graphs - A Survey
Graphs and Combinatorics
Automata with extremal minimality conditions
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Some remarks on automata minimality
DLT'11 Proceedings of the 15th international conference on Developments in language theory
A graph theoretic approach to automata minimality
Theoretical Computer Science
Extremal minimality conditions on automata
Theoretical Computer Science
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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.