Geodesic
Matrix characterization of symmetry groups of boolean functions
Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 71-83.

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We studies symmetry groups of boolean functions and construct new way of description of this problem in matrices language. Some theorems about constructions of symmetry groups with using matrices are presented. Some properties of this approach are given.
Mots-clés : Boolean function, invariance group, symmetry group. 
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Pawel Jasionowski. Matrix characterization of symmetry groups of boolean functions. Algebra and discrete mathematics, Tome 14 (2012) no. 1, pp. 71-83. https://geodesic-test.mathdoc.fr/item/ADM_2012_14_1_a6/

[1] N. L. Biggs, A. T. White, Permutation groups and combinatorial structures, London Math. Soc., Lecture Notes Series, 33, Cambridge Univ. Press, Cambridge, 1979 | MR | Zbl

[2] P. Cameron, Permutation Groups, Cambridge University Press, Cambridge, 1999 | MR

[3] P. Clote, E. Kranakis, “Boolean function invariance groups, and parallel complexity”, J. Comput., 20:3 (1991), 553–590 | MR | Zbl

[4] P. Clote, E. Kranakis, Boolean function and Computation Models, Springer, Berlin, 2002 | MR | Zbl

[5] M. Grech, A. Kisielewicz, “Direct product of automorphism groups of colored graphs”, Discrete Math., 283 (2004), 81–86 | DOI | MR | Zbl

[6] M. Grech, “Regular symmetric groups of boolean function”, Discrete Math., 310 (2010), 2877–2882 | DOI | MR | Zbl

[7] A. Kisielewicz, “Symmetry groups of Boolean functions and constructions of permutation groups”, Journal of Algebra, 199 (1998), 379–403 | DOI | MR | Zbl

[8] W. Peisert, “Direct product and uniqueness of automorphism groups of graphs”, Discrete Math., 207 (1999), 189–197 | DOI | MR | Zbl

[9] H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964 | MR | Zbl

[10] W. Xiao, “Linear symmetries of Boolean functions”, Discrete Applied Math., 149 (2005), 192–199 | DOI | MR | Zbl