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Learning Restricted Deterministic Regular Expressions with Counting

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Book cover Web Information Systems Engineering – WISE 2019 (WISE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11881))

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Abstract

Regular expressions are widely used in various fields. Learning regular expressions from sequence data is still a popular topic. Since many XML documents are not accompanied by a schema, or a valid schema, learning regular expressions from XML documents becomes an essential work. In this paper, we propose a restricted subclass of single-occurrence regular expressions with counting (RCsores) and give a learning algorithm of RCsores. First, we learn a single-occurrence regular expressions (SORE). Then, we construct an equivalent countable finite automaton (CFA). Next, the CFA runs on the given finite sample to obtain an updated CFA, which contains counting operators occurring in an RCsore. Finally we transform the updated CFA to an RCsore. Moreover, our algorithm can ensure the result is a minimal generalization (such generalization is called descriptive) of the given finite sample.

Work supported by National Natural Science Foundation of China under Grant Nos. 61872339, 61472405.

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Notes

  1. 1.

    http://schemas.opengis.net/.

  2. 2.

    For instance, the original expression in XSD can be denoted by \(r_0=(a|b)^{[1,6]}\), given sample \(\{ba,aa,abaa,aabaa\}\), the ECsore learnt by InfECsore is \(r_1=(b?a^{[1,2]})^{[1,2]}\). However, the learnt RCsore can be \(r_2=(b?a)^{[1,4]}\). Let \(S_1\!=\!\{s|s\!\in \! \mathcal {L}(r_0),s\!\in \! \mathcal {L}(r_1)\}\) and \(S_2\!=\!\{s|s\!\in \! \mathcal {L}(r_0),s\!\in \! \mathcal {L}(r_2)\}\). Then, \(|S_1|\!=\!14\) and \(|S_2|\!=\!25\). Thus, \(\frac{|S_1|}{|\mathcal {L}(r_0)|}<\frac{|S_2|}{|\mathcal {L}(r_0)|}\).

  3. 3.

    Let \(S\!=\!\{b,abd,ad,cddcdd\}\), the cSORE learnt by InfcSORE is \(r_3\!=\!((a?b?|c)d?)^{[1,4]}\), however, there is a cSORE \(r_4\!=\!(a?b?|c?(d^{[1,2]})?)^{[1,2]}\) such that \(\mathcal {L}(r_3)\!\supset \!\mathcal {L}(r_4)\!\supseteq \!S\).

  4. 4.

    Note that, the CFA \(\mathcal {A}\) runs on S, the direct counting result for b is \((l(b),u(b))\!=\!(1,2)\). However, (l(b), u(b)) is subsequently updated by Counting that b can be repeated by using the counting operator \([l(+_2),u(+_2)]\!=\![1,3]\).

  5. 5.

    http://dblp.org/xml/release/.

  6. 6.

    http://www.dbis.informatik.uni-goettingen.de/Mondial/#XML.

  7. 7.

    http://www.cs.toronto.edu/tox/toxgene/.

  8. 8.

    http://schemas.opengis.net/.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaofan Wang & Haiming Chen

  2. University of Chinese Academy of Sciences, Beijing, China

    Xiaofan Wang

Authors
  1. Xiaofan Wang
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  2. Haiming Chen
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Correspondence to Haiming Chen .

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Editors and Affiliations

  1. University of Hong Kong, Hong Kong SAR, China

    Reynold Cheng

  2. University of Ioannina, Ioannina, Greece

    Nikos Mamoulis

  3. University of California, Los Angeles, CA, USA

    Yizhou Sun

  4. Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China

    Xin Huang

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Wang, X., Chen, H. (2019). Learning Restricted Deterministic Regular Expressions with Counting. In: Cheng, R., Mamoulis, N., Sun, Y., Huang, X. (eds) Web Information Systems Engineering – WISE 2019. WISE 2020. Lecture Notes in Computer Science(), vol 11881. Springer, Cham. https://doi.org/10.1007/978-3-030-34223-4_7

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  • DOI: https://doi.org/10.1007/978-3-030-34223-4_7

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