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原文摘要

The regular cover problem is the following question: given a finite language $L$ and a $k\geq 0$, is there an acyclic regular grammar $G$ with at most $k$ productions that covers $L$, i.e., that satisfies $L(G) \supseteq L$. The study of this problem is motivated by applications in proof theory and automated deduction. The regular cover problem is known to be in NP. In this paper we show that it is NP-complete by reducing the vertex cover problem for graphs with maximum degree three to it.