Abstract
While the edit-distance neighborhood is useful for approximate pattern matching, it is not suitable for the negative lookahead feature for the practical regex matching engines. This motivates us to introduce a new operation. We define the edit-distance interior operation on a language L to compute the largest subset I(L) of L such that the edit-distance neighborhood of I(L) is in L. In other words, L includes the edit-distance neighborhood of the largest edit-distance interior language. Given an edit-distance value r, we show that the radius-r edit-distance interior operation is a weak inverse of the radius-r edit-distance neighborhood operation, and vice versa. In addition, we demonstrate that regular languages are closed under the edit-distance interior operation whereas context-free languages are not. Then, we characterize the edit-distance interior languages and present a proper hierarchy with respect to the radius of operations. The family of edit-distance interior languages is closed under intersection, but not closed under union, complement and catenation.
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Acknowledgments
This research was supported by the NRF grant (RS-2023-00208094). We wish to thank the anonymous reviewers for their valuable suggestions.
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Cheon, H., Han, YS. (2023). Weak Inverse Neighborhoods of Languages. In: Drewes, F., Volkov, M. (eds) Developments in Language Theory. DLT 2023. Lecture Notes in Computer Science, vol 13911. Springer, Cham. https://doi.org/10.1007/978-3-031-33264-7_6
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DOI: https://doi.org/10.1007/978-3-031-33264-7_6
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