确定性上下文无关语言的交与并层次及泵引理
摘要
我们研究确定性上下文无关(dcf)语言的有限交与有限并的计算复杂性。早前，Wotschke [J. Comput. System Sci. 16 (1978) 456--461]基于Liu与Weiner [Math. Systems Theory 7 (1973) 185--192]的交层次分离结果，证明了对任意正整数，个dcf语言的交一般比个dcf语言的交更强。然而，Liu与Weiner的论证仅适用于特定形式的有限语言，因此Wotschke的结果不能直接推广到其他非有限语言。为处理不属于交层次的大量语言，我们规避其证明技术的特殊性，并设计了一种新颖且实用的技术工具：用于dcf语言有限并的两个泵引理。由于dcf语言族在补运算下封闭，也在与正则语言的交运算下封闭，这些泵引理有助于我们确立由目标语言的有限交构成语言的非隶属关系。我们亦关注此情形下其与Hibbard [Inf. Control 11 (1967) 196--238]的确定性受限自动机的关系。
引用
@article{arxiv.2112.09383,
title = {Intersection and Union Hierarchies of Deterministic Context-Free Languages and Pumping Lemmas},
author = {Tomoyuki Yamakami},
journal= {arXiv preprint arXiv:2112.09383},
year = {2025}
}
备注
(A4, 10pt, p.30, 5 figure) This exposition completes and corrects a preliminary report that appeared in the Proceedings of the 14th International Conference on Language and Automata Theory and Applications (LATA 2020), Lecture Notes in Computer Science, vol. 12038, pp. 341-353, 2020. A conference talk was given online during October 20-24, 2021 due to the coronavirus pandemic