Abstract
We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.
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References
Alperin, J.L., Bell, R.B.: Groups and Representations. Springer (1995)
Delgado, M., Egri-Nagy, A., Mitchell, J.D., Pfeiffer, M.: VIZ – GAP package for visualisation (2014), https://bitbucket.org/james-d-mitchell/viz
Dini, P., Nehaniv, C.L., Egri-Nagy, A., Schilstra, M.J.: Exploring the concept of interaction computing through the discrete algebraic analysis of the belousov-zhabotinsky reaction. Biosystems 112(2), 145–162 (2013), Selected papers from the 9th International Conference on Information Processing in Cells and Tissues
Dömösi, P., Nehaniv, C.L.: Algebraic Theory of Finite Automata Networks: An Introduction. SIAM Series on Discrete Mathematics and Applications, vol. 11. Society for Industrial and Applied Mathematics (2005)
Egri-Nagy, A., Nehaniv, C.L.: Cascade Product of Permutation Groups. arXiv:1303.0091v3 [math.GR] (2013), http://arxiv.org/abs/1303.0091
Egri-Nagy, A., Nehaniv, C.L., Mitchell, J.D.: SgpDec – software package for hierarchical decompositions and coordinate systems, Version 0.7+ (2013), http://sgpdec.sf.net
Eilenberg, S.: Automata, Languages and Machines, vol. B. Academic Press (1976)
Ellson, J., Gansner, E.R., Koutsofios, E., North, S.C., Woodhull, G.: Graphviz and dynagraph static and dynamic graph drawing tools. In: Graph Drawing Software, pp. 127–148. Springer (2003)
The GAP Group: GAP – Groups, Algorithms, and Programming, Version 4.7.1 (2013), http://www.gap-system.org
Ginzburg, A.: Algebraic Theory of Automata. Academic Press (1968)
Holcombe, W.M.L.: Algebraic Automata Theory. Cambridge University Press (1982)
Holt, D., Eick, B., O’Brien, E.: Handbook of Computational Group Theory. CRC Press (2005)
Krasner, M., Kaloujnine, L.: Produit complet des groupes de permutations et problème d’ extension de groupes. Acta Scientiarium Mathematicarum (Szeged) 14, 39–66 (1951)
Krohn, K., Rhodes, J.: Algebraic Theory of Machines. I. Prime Decomposition Theorem for Finite Semigroups and Machines. Transactions of the American Mathematical Society 116, 450–464 (1965)
Wells, C.: A Krohn-Rhodes theorem for categories. Journal of Algebra 64, 37–45 (1980)
Paul Zeiger, H.: Cascade synthesis of finite state machines. Information and Control 10, 419–433 (1967), plus erratum
Paul Zeiger, H.: Cascade Decomposition Using Covers. In: Arbib, M.A. (ed.) Algebraic Theory of Machines, Languages, and Semigroups, ch. 4, pp. 55–80. Academic Press (1968)
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Egri-Nagy, A., Mitchell, J.D., Nehaniv, C.L. (2014). SgpDec: Cascade (De)Compositions of Finite Transformation Semigroups and Permutation Groups. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_13
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DOI: https://doi.org/10.1007/978-3-662-44199-2_13
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