Abstract
We present a distance metric on formal languages based on the accumulated weight of words in their symmetric difference. The contribution of an individual word to this weight decreases exponentially in its length, guaranteeing the distance between languages to be a real value between 0 and 1. We show that this distance is computable for regular languages. As an application, we show how the similarity measure derived from a modification of this metric can be used in automatic grading of particular standard exercises in formal language theory classes.
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Actual matrix multiplication can be done in time \(\mathcal {O}(|Q|^{2.37286})\), cf. e.g. [1]. We state the cubic runtime here for the sake of readability.
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Bruse, F., Herwig, M., Lange, M. (2022). A Similarity Measure for Formal Languages Based on Convergent Geometric Series. In: Caron, P., Mignot, L. (eds) Implementation and Application of Automata. CIAA 2022. Lecture Notes in Computer Science, vol 13266. Springer, Cham. https://doi.org/10.1007/978-3-031-07469-1_6
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DOI: https://doi.org/10.1007/978-3-031-07469-1_6
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