On the distribution of the number of monotone boolean functions relative to the number of lower units

Authors:
A. D. Korshunov;I. Shmulevich
Affiliations:
Sobolev Institute of Mathematics, Pr. Akad. Koptyuga, 4, 630090 Novosibirsk, Russia;Tampere International Center for Signal Processing, Tampere University of Technology, Tampere, Finland and Department of Pathology, University of Texas M.D. Anderson Cancer Center, Box 85, 1515 Ho ...
Venue:
Discrete Mathematics - Kleitman and combinatorics: a celebration
Year:
2002

Citing 5
Cited 2

Properties of complexity measures for prams and wrams

Theoretical Computer Science
On the Fourier spectrum of monotone functions

Journal of the ACM (JACM)
Interactive learning of monotone Boolean functions

Information Sciences: an International Journal
The Maximum Latency and Identification of Positive Boolean Functions

SIAM Journal on Computing
OBDDs of a Monotone Function and of Its Prime Implicants

ISAAC '96 Proceedings of the 7th International Symposium on Algorithms and Computation

Identification of fuzzy measures from sample data with genetic algorithms

Computers and Operations Research
Singleton and 2-periodic attractors of sign-definite Boolean networks

Information Processing Letters

Quantified Score

Hi-index	0.01

Visualization

Abstract

We find asymptotic formulae for the number of monotone Boolean functions of n variables with a most probable number of terms in the minimal disjunctive normal form. It is proven that the distribution of such functions is asymptotically normal if all monotone Boolean functions are equiprobable. The formulae are different depending on whether n is even or odd.