On the Classification of Boolean Functions by the General Linear and Affine Groups
Michael A. Harrison · Journal of the Society for Industrial and Applied Mathematics · 1964
Previous article Next article On the Classification of Boolean Functions by the General Linear and Affine GroupsMichael A. HarrisonMichael A. Harrisonhttps://doi.org/10.1137/0112026PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957x+214 MR0082463 (18,553e) 0077.02101 Google Scholar[2] Robert L. Ashenhurst, The application of counting techniques, Proceedings of the Association for Computing Machinery, Pittsburgh, 1952, Richard Rimbach Associates, Pittsburgh, Pa., 1952, 293–305 MR0056562 (15,93h) Google Scholar[3] Randolph Church, Tables of irreducible polynomials for the first four prime moduli, Ann. of Math. (2), 36 (1935), 198–209 MR1503219 0011.00501 CrossrefGoogle Scholar[4] Leonard Eugene Dickson, Linear groups: With an exposition of the Galois field theory, with an introduction by W. Magnus, Dover Publications Inc., New York, 1958xvi+312 MR0104735 (21:3488) 0082.24901 Google Scholar[5] B. Elspas, Autonomous linear sequential networks, I. R. E. Trans., CT-6 (1959), 45–60, March Google Scholar[6] Michael A. Harrison, The number of transitivity sets of Boolean functions, J. Soc. Indust. Appl. Math., 11 (1963), 521–525 10.1137/0111037 MR0157826 (28:1055) 0119.01202 LinkISIGoogle Scholar[7] M. A. Harrison, Ph.D. Thesis, Combinatorial problems in Boolean algebras and applications to the theory of switching, University of Michigan, 1963 Google Scholar[8] M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Prof. Group of Electronic Computers, (1963), , September 0129.01405 CrossrefGoogle Scholar[9] Michael A. Harrison, The number of classes of invertible Boolean functions, J. Assoc. Comput. Mach., 10 (1963), 25–28 MR0151399 (27:1384) 0126.00901 CrossrefISIGoogle Scholar[10] L. Hellerman, Equivalence classes of logical functions, IBM Tech. Pub. TROO. 819, 1961, November Google Scholar[11] C. S. Lorens, Invertible Boolean functions, Space General Corporation Report, 1962, July Google Scholar[12] K. S. Menger, A modulo two adder for three inputs using a single tunnel diode, I. R. E. Trans., 10 (1961), 530–531 Google Scholar[13] E. I. Nechiporuk, On the synthesis of networks using linear transformations of variables, Dokl. Akad. Nauk. SSSR, 123 (1958), 610–612, Available in English in Automation Express, April 1959, pp. 12–13 0089.12805 Google Scholar[14] G. Pólya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen, und chemische Verbindungen, Acta Math., 68 (1937), 145–253 0017.23202 CrossrefGoogle Scholar[15] G. Pólya, Sur les types des propositions composées, J. Symbolic Logic, 5 (1940), 98–103 MR0002510 (2,65d) 0024.00102 CrossrefGoogle Scholar[16] David Slepian, On the number of symmetry types of Boolean functions of n variables, Canadian J. Math., 5 (1953), 185–193 MR0056560 (15,93f) 0051.24802 CrossrefISIGoogle Scholar[17] David Slepian, Some further theory of group codes, Bell System Tech. J., 39 (1960), 1219–1252 MR0122628 (22:13351) CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Boolean Functions, Invariance Groups, and Parallel Complexity13 July 2006 | SIAM Journal on Computing, Vol. 20, No. 3AbstractPDF (4442 KB) Volume 12, Issue 2| 1964Journal of the Society for Industrial and Applied Mathematics History Submitted:02 October 1962Published online:28 July 2006 InformationCopyright © 1964 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0112026Article page range:pp. 285-299ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics