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Recognition of Whitehead-Minimal Elements in Free Groups of Large Ranks

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Artificial Intelligence and Symbolic Computation (AISC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3249))

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Abstract

In this paper we introduce a pattern classification system to recognize words of minimal length in their automorphic orbits in free groups. This system is based on Support Vector Machines and does not use any particular results from group theory. The main advantage of the system is its stable performance in recognizing minimal elements in free groups with large ranks.

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References

  1. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table. Dover Publications, Inc., New York (1972)

    Google Scholar 

  2. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley Interscience, Hoboken (2000)

    Google Scholar 

  3. Haykin, S.: Neural networks: A comprehensive foundation. Prentice Hall, Upper Sadle River (1999)

    MATH  Google Scholar 

  4. Kapovich, I., Schupp, P., Shpilrain, V.: Generic properties of whitehead’s algorithm, stabilizers in aut(fk)and one-relator groups (2003) (preprint)

    Google Scholar 

  5. Miasnikov, A.D., Haralick, R.M.: Regression analysis and automorphic orbits in free groups of Rank 2. In: 17th International Conference on Pattern Recognition (2004) (to appear)

    Google Scholar 

  6. Miasnikov, A.D., Myasnikov, A.G.: Whitehead method and genetic algorithms. Contemporary Mathematics 349, 89–114 (2004)

    MathSciNet  Google Scholar 

  7. Haralick, R.M., Miasnikov, A.D., Myasnikov, A.G.: Pattern Recognition Approaches to Solving Combinatorial Problems in Free Groups. Contemporary Mathematics 349, 197–213 (2004)

    MathSciNet  Google Scholar 

  8. L. R., Schupp, P.: Combinatorial Group Theory. Series of Modern Studies in Math, vol. 89. Springer, Heidelberg (1977)

    MATH  Google Scholar 

  9. Vapnik, V.N.: Statistical Learning Theory. John Wiley and Sons, New York (1998)

    MATH  Google Scholar 

  10. Vapnik, V.N.: The nature of statistical learning theory. Springer, New York (2000)

    MATH  Google Scholar 

  11. Whitehead, J.H.C.: On equivalent sets of elements in a free group. Annals of Mathematic 37(4), 782–800 (1936)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. The Graduate Center of CUNY, Computer Science, 365 5th ave, New York, USA

    Alexei D. Miasnikov

Authors
  1. Alexei D. Miasnikov
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Editor information

Editors and Affiliations

  1. Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria

    Bruno Buchberger

  2. Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK

    John Campbell

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© 2004 Springer-Verlag Berlin Heidelberg

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Miasnikov, A.D. (2004). Recognition of Whitehead-Minimal Elements in Free Groups of Large Ranks. In: Buchberger, B., Campbell, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2004. Lecture Notes in Computer Science(), vol 3249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30210-0_18

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  • DOI: https://doi.org/10.1007/978-3-540-30210-0_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23212-4

  • Online ISBN: 978-3-540-30210-0

  • eBook Packages: Springer Book Archive

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