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Deriving Formulas for Integer Sequences Using Inductive Programming

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Artificial Intelligence (BNAIC 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1021))

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Abstract

Solving integer sequences, correctly predicting the next number in a given sequence, is a challenging task for both humans and artificial intelligence. We present a method to derive a formula for an integer sequence given a subsequence. By splitting the known subsequence into ‘windows’, we can derive constraints in the form of linear combinations, which can be generalised to find a formula for the complete sequence. This approach is effective and can compete with existing methods based on pattern recognition and Artificial Neural Networks with regard to performance, success rate, and output quality.

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Notes

  1. 1.

    Note that n can often be infinite.

References

  1. Düsel, M., Werner, A., Zeißner, T.: Solving number series with the MagicHaskeller. Technical report, University of Bamberg (2012)

    Google Scholar 

  2. Hernández-Orallo, J., Martínez-Plumed, F., Schmid, U., Siebers, M., Dowe, D.L.: Computer models solving intelligence test problems: progress andimplications. Artif. Intell. 230, 74–107 (2016). https://doi.org/10.1016/j.artint.2015.09.011. http://www.sciencedirect.com/science/article/pii/S0004370215001538

    Article  Google Scholar 

  3. Milovec, M.: Applying inductive programming to solving number series problems. Master’s thesis, University of Bamberg (2014)

    Google Scholar 

  4. OEIS Foundation Inc.: The Online Encyclopedia of Integer Sequences (2018). https://oeis.org/

  5. Ragni, M., Klein, A.: Predicting numbers: an AI approach to solving number series. In: Bach, J., Edelkamp, S. (eds.) KI 2011. LNCS (LNAI), vol. 7006, pp. 255–259. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24455-1_24

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Acknowledgements

We would like to thank our supervisor Prof. Luc De Raedt for his guidance and support during our bachelor’s thesis.

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Authors and Affiliations

  1. Department of Computer Science, KU Leuven, 3000, Leuven, Belgium

    Les De Ridder & Thijs Vercammen

Authors
  1. Les De Ridder
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  2. Thijs Vercammen
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Corresponding author

Correspondence to Les De Ridder .

Editor information

Editors and Affiliations

  1. Tilburg University, Tilburg, The Netherlands

    Martin Atzmueller

  2. Eindhoven University of Technology, Eindhoven, The Netherlands

    Wouter Duivesteijn

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De Ridder, L., Vercammen, T. (2019). Deriving Formulas for Integer Sequences Using Inductive Programming. In: Atzmueller, M., Duivesteijn, W. (eds) Artificial Intelligence. BNAIC 2018. Communications in Computer and Information Science, vol 1021. Springer, Cham. https://doi.org/10.1007/978-3-030-31978-6_2

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  • DOI: https://doi.org/10.1007/978-3-030-31978-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31977-9

  • Online ISBN: 978-3-030-31978-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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