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No Shannon effect on probability distributions on Boolean functions induced by random expressions
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010).

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The Shannon effect states that "almost all'' Boolean functions have a complexity close to the maximal possible for the uniform probability distribution. In this paper we use some probability distributions on functions, induced by random expressions, and prove that this model does not exhibit the Shannon effect. 
@article{DMTCS_2010_special_258_a20,
     author = {Genitrini, Antoine and Gittenberger, Bernhard},
     title = {No {Shannon} effect on probability distributions on {Boolean} functions induced by random expressions},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10)},
     year = {2010},
     doi = {10.46298/dmtcs.2784},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2784/}
}
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Genitrini, Antoine; Gittenberger, Bernhard. No Shannon effect on probability distributions on Boolean functions induced by random expressions. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10), DMTCS Proceedings vol. AM, 21st International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'10) (2010). doi : 10.46298/dmtcs.2784. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2784/

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