Computational Understanding and Manipulation of Symmetries

  • Attila Egri-Nagy
  • Chrystopher L. Nehaniv
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8955)


For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. This algebraic coordinatization is based on a hierarchical (de)composition method. Here we describe this method and apply it to permutation puzzles. Coordinatization yields a structural understanding, not just solutions for the puzzles. In the case of the Rubik’s Cubes, different solving strategies correspond to different decompositions.


permutation puzzle wreath product coordinatization cascade decomposition Rubik’s Cube 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Attila Egri-Nagy
    • 1
    • 2
  • Chrystopher L. Nehaniv
    • 1
  1. 1.Centre for Computer Science and Informatics ResearchUniversity of HertfordshireHatfieldUnited Kingdom
  2. 2.Centre for Research in Mathematics,School of Computing, Engineering and MathematicsUniversity of Western SydneyPenrithAustralia

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