Geodesic
On circuits of functional elements of finite depth of branching
Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 73-83

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We introduce the notion of the depth of branching of a circuit of functional elements and consider classes of circuits of branching depth bounded by a constant. For these classes of circuits over various bases we obtain lower and upper bounds for complexity of a linear Boolean function. We construct infinitely decreasing sequences of measures of complexity for a fixed base and growing branching depth and for a fixed branching depth but varying base. 
@article{DM_2006_18_4_a6,
     author = {D. Yu. Cherukhin},
     title = {On circuits of functional elements of finite depth of branching},
     journal = {Diskretnaya Matematika},
     pages = {73--83},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2006_18_4_a6/}
}
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D. Yu. Cherukhin. On circuits of functional elements of finite depth of branching. Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 73-83. http://geodesic.mathdoc.fr/item/DM_2006_18_4_a6/