Summary form only given, as follows. The minimum consistent DFA problem is that of finding a DFA with as few states as possible that is consistent with a given sample (a finite collection of words, each labeled as to whether the DFA found should accept or reject). Assuming that P not=NP, it is shown that for any constant k, no polynomial-time algorithm can be guaranteed to find a consistent DFA of size opt/sup k/, where opt is the size of a smallest DFA consistent with the sample. This result holds even if the alphabet is of constant size two and if the algorithm is allowed to produce an NFA, a regular grammar, or a regular expression that is consistent with the sample. Similar hardness results are presented for the problem of finding small consistent linear grammars.
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机译:仅给出摘要表格,如下。最小的DFA一致性问题是找到一个与给定样本(状态有限的单词集合,每个单词都标明找到的DFA应该接受还是拒绝)相一致的尽可能少的状态的DFA。假设P not = NP,表明对于任何常数k,都不能保证多项式时间算法能够找到大小opt / sup k /的一致DFA,其中opt是与样本一致的最小DFA的大小。即使字母表的大小恒定为2,并且允许算法生成与样本一致的NFA,正则语法或正则表达式,该结果也成立。对于找到小的一致线性语法的问题,也给出了相似的硬度结果。
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