Geodesic
Depth of $\alpha$-completions of systems of Boolean functions
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 72-75

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A problem of implementation of Boolean functions by $\alpha$-formulas is considered. These formulas are such that each subformula contains not more that one nontrivial principal subformula. The depth is considered as a complexity measure of a formula. Upper and lower polynomial estimates of Shannon functions for $\alpha$-supplements of finite systems of Boolean functions are obtained. 
@article{VMUMM_2009_2_a15,
     author = {D. V. Truschin},
     title = {Depth of $\alpha$-completions of systems of {Boolean} functions},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {72--75},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a15/}
}
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D. V. Truschin. Depth of $\alpha$-completions of systems of Boolean functions. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2009), pp. 72-75. http://geodesic.mathdoc.fr/item/VMUMM_2009_2_a15/