Geodesic
On the complexity and depth of circuits realizing partial Boolean functions
Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 53-58.

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The complexity and depth of circuits that realize partial Boolean functions are studied under the assumption that $FP\neq NC$. It is established that there exist partial Boolean functions for which the complexity and depth of circuits cannot be simultaneously close to the minimally possible values, i.e., any circuit realizing such a function has either a depth or a complexity that considerably exceeds either the depth or the complexity of the function which it realizes. 
@article{DM_1997_9_2_a4,
     author = {A. V. Chashkin},
     title = {On the complexity and depth of circuits realizing partial {Boolean} functions},
     journal = {Diskretnaya Matematika},
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     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_2_a4/}
}
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A. V. Chashkin. On the complexity and depth of circuits realizing partial Boolean functions. Diskretnaya Matematika, Tome 9 (1997) no. 2, pp. 53-58. http://geodesic.mathdoc.fr/item/DM_1997_9_2_a4/