Abstract
We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rectifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G) ≥ Rect(G)3/2 − ε. As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with ε-transitions, having n transitions total such that the smallest equivalent ε-free NFA has Ω(n 3/2 − ε) transitions. We also formulate a version of previous bounds for the weighted set cover problem and discuss its connections to giving upper bounds for the possible blow-up.
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Iván, S., Lelkes, Á.D., Nagy-György, J., Szörényi, B., Turán, G. (2014). Biclique Coverings, Rectifier Networks and the Cost of ε-Removal. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_16
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DOI: https://doi.org/10.1007/978-3-319-09704-6_16
Publisher Name: Springer, Cham
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