On the asymptotics of the number of repetition-free Boolean functions in the basis {&, ∨, ⊕, ¬}
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Vitaliy A. Voblyi
Abstract
We obtain an asymptotic formula for the number Sn of repetition-free Boolean functions of n variables in the basis {&, ∨, ⊕, ¬} for n → ∞ : Sn ∼ cn−3/2αnn!, where c ≈ 0.1998398363, α ≈ 7.549773429.
Originally published in Diskretnaya Matematika (2015) 27, №3, 158–159 (in Russian).
Acknowledgement
The author is grateful to the anonymous reviewer for suggestions permitting to improve the presentation of results.
References
[1] Selected aspects of the Boolean functions theory, eds. S. F. Vinokurov, N. A. Peryazev, Fizmatlit, Moscow, 2001 (In Russian), 192 pp.Search in Google Scholar
[2] Zubkov O. V., “Refined estimates of the number of repetition-free Boolean functions in the full binary basis {&, ∨, ⊕, ¬}”, Mathematical Notes, 87:5 (2010), 687–699.10.1134/S0001434610050081Search in Google Scholar
[3] Voblyi V. A., “The asymptotics of the number of repetition-free Boolean functions in the basis B1”, Discrete Math. Appl., 20:5 (2010), 707–708.10.1515/dma.2010.043Search in Google Scholar
[4] Lavrentiev M. A., Shabat B. M., Methods of a theory of functions of complex variable, Nauka, Moscow, 1965 (In Russian), 716 pp.Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- An approach to the transformation of periodic sequences
- On the number of functions of k-valued logic which are polynomials modulo composite k
- Upper bounds for the size and the depth of formulae for MOD-functions
- Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set
- The second coordinate sequence of the MP-LRS over nontrivial Galois ring of an odd characteristic
- On the asymptotics of the number of repetition-free Boolean functions in the basis {&, ∨, ⊕, ¬}
- On the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates
Articles in the same Issue
- Frontmatter
- An approach to the transformation of periodic sequences
- On the number of functions of k-valued logic which are polynomials modulo composite k
- Upper bounds for the size and the depth of formulae for MOD-functions
- Mean and variance of the number of subfunctions of random Boolean function which are close to the affine functions set
- The second coordinate sequence of the MP-LRS over nontrivial Galois ring of an odd characteristic
- On the asymptotics of the number of repetition-free Boolean functions in the basis {&, ∨, ⊕, ¬}
- On the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates
