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Grammatical Inference in the Discovery of Generating Functions

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Man–Machine Interactions 4

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 391))

Abstract

In this paper an algorithm for the induction of a context-free grammar is proposed, and its application in obtaining a generating function for the number of certain combinatorial objects is demonstrated. In particular, two problems classified in The On-Line Encyclopedia of Integer Sequences (http://oeis.org/) under entries A000073 and A000108, as well as a problem from the domain of chemoinformatics, are solved as an illustration of our method.

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Notes

  1. 1.

    Our translation can be further re-formulated as an integer linear program, but the number of variables increases so much that this is not profitable.

  2. 2.

    To expand this fraction in a power series, one can use Maclaurin’s formula:

    $$\begin{aligned} f(z) = f(0) + \frac{z}{1!} f'(0) + \frac{z^2}{2!} f''(0) + \cdots + \frac{z^n}{n!} f^{(n)}(0) + \cdots \ . \end{aligned}$$
  3. 3.

    Recall that we hope to obtain grammars that are likely to be unambiguous.

  4. 4.

    We are aware of this imprecision. The number of words and their lengths should allow of executing a program in a reasonable amount of time. This, in turn, depends on many circumstances.

  5. 5.

    To model and solve our non-linear program we make use of the Optimization Modeling Language (OML) and Microsoft Solver Foundation 3.1 development tools.

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Acknowledgments

This research was supported in part by PL-Grid Infrastructure, and by Grant No. DEC-2011/03/B/ST6/01588 from National Science Center of Poland.

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Authors and Affiliations

  1. Institute of Computer Science, University of Silesia, Sosnowiec, Poland

    Wojciech Wieczorek & Arkadiusz Nowakowski

Authors
  1. Wojciech Wieczorek
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  2. Arkadiusz Nowakowski
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Corresponding author

Correspondence to Wojciech Wieczorek .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Aleksandra Gruca

  2. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Agnieszka Brachman

  3. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Stanisław Kozielski

  4. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Tadeusz CzachĂłrski

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Wieczorek, W., Nowakowski, A. (2016). Grammatical Inference in the Discovery of Generating Functions. In: Gruca, A., Brachman, A., Kozielski, S., Czachórski, T. (eds) Man–Machine Interactions 4. Advances in Intelligent Systems and Computing, vol 391. Springer, Cham. https://doi.org/10.1007/978-3-319-23437-3_54

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  • DOI: https://doi.org/10.1007/978-3-319-23437-3_54

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