

A000370


Number of NPNequivalence classes of Boolean functions of n or fewer variables.
(Formerly M1287 N0494)


9




OFFSET

0,2


COMMENTS

Number of Boolean functions distinct under complementation/permutation.


REFERENCES

M. A. Harrison, Introduction to Switching and Automata Theory. McGraw Hill, NY, 1965, p. 153.
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.
S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38, Table 2.3.2.  Row 16.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..8.
M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559561.
M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559561. [Annotated scanned copy]
M. A. Harrison, On asymptotic estimates in switching and automata theory, J. ACM, v. 13, no. 1, Jan. 1966, pp. 151157.
S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]
S. Muroga, T. Tsuboi and C. R. Baugh, Enumeration of threshold functions of eight variables, IEEE Trans. Computers, 19 (1970), 818825. [Annotated scanned copy]
Juling Zhang, Guowu Yang, William N. N. Hung, Tian Liu, Xiaoyu Song, Marek A. Perkowski, A Group Algebraic Approach to NPN Classification of Boolean Functions, Theory of Computing Systems (2018), 120.
Index entries for sequences related to Boolean functions


FORMULA

a(n) is asymptotic to 2^{2^n} / ( n! * 2^{n+1} ) as n > oo. This follows from a theorem of Michael Harrison. See Theorem 3 in Harrison (JACM, 1966).  Eric Bach, Aug 07 2017


CROSSREFS

Sequence in context: A134040 A061291 A166105 * A326941 A132531 A123052
Adjacent sequences: A000367 A000368 A000369 * A000371 A000372 A000373


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Vladeta Jovovic, Feb 23 2000


STATUS

approved



