正则语言的渐近概率几乎等价性及其计算复杂性
The Almost Equivalence by Asymptotic Probabilities for Regular Languages and Its Computational Complexities
摘要：
本文利用渐近概率引入p-等价，这是有限模型理论中基于零-一定律的弱几乎等价。本文研究了正则语言的p-等价问题的计算复杂性，并给出了以下细节。首先，我们给出了p-等价的鲁棒性和p-等价的逻辑刻画。这一刻画有助于通过与描述复杂性的标准结果耦合来生成p-等价问题的一些算法。其次，我们给出了p-等价问题的计算复杂性。计算复杂性与（完全）等价问题相同。最后，我们将p-等价的证明应用到一些广义等价上。
英文摘要：
We introduce p-equivalence by asymptotic probabilities, which is a weak almost-equivalence based on zero-one laws in finite model theory. In this paper, we consider the computational complexities of p-equivalence problems for regular languages and provide the following details. First, we give an robustness of p-equivalence and a logical characterization for p-equivalence. The characterization is useful to generate some algorithms for p-equivalence problems by coupling with standard results from descriptive complexity. Second, we give the computational complexities for the p-equivalence problems by the logical characterization. The computational complexities are the same as for the (fully) equivalence problems. Finally, we apply the proofs for p-equivalence to some generalized equivalences.
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