The Almost Equivalence by Asymptotic Probabilities for Regular Languages and Its Computational Complexities

• Main Author: Yoshiki Nakamura
• Format: Article
• Language: English
• Published: Open Publishing Association 2016-09-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1609.04101v1

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.